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Understanding Bits and Bytes: Exploring Data Representation

Understanding Bits and Bytes

Hey there, tech-savvy pals! Today, we’re going to unravel the mysteries of data representation by delving into the realm of bits and bytes. 🤓 Let’s break it down like never before!

Definition of Bits and Bytes

First things first, let’s talk about what bits and bytes actually are. Bits are the smallest units of data in computing, represented as either a 0 or a 1. On the other hand, a byte consists of 8 bits . Yep, you heard that right, 8 bits cozying up together in a byte!

Purpose and Importance of Understanding Bits and Bytes

Now, you might be wondering, “Why do I need to wrap my head around these bits and bytes?” Well, buckle up because understanding them is like holding the key to a secret coding treasure chest! From programming to data storage , bits and bytes are the building blocks of the digital world.

Data Representation with 8 Bits in a Byte

Understanding the binary system.

Ah, the binary system, where everything boils down to 0s and 1s. It’s like the yin and yang of the computing world, representing off and on states. With just two digits, the binary system works wonders in storing and processing data efficiently .

How 8 Bits in a Byte Represent Data

Picture this: each bit in a byte is like a tiny switch that can either be off (0) or on (1). By combining 8 of these switches, we can create unique patterns to represent different characters, numbers, or instructions in a computer.

Number of Possible Values with 8 Bits in a Byte

Understanding the concept of combinations and permutations.

Now, let’s dive into the math realm for a bit. To calculate the number of possible values with 8 bits in a byte, we need to unleash the power of combinations and permutations. It’s all about the art of arranging those 0s and 1s in various ways!

Calculation of Possible Values with 8 Bits in a Byte

So, the burning question is, how many possible values can we have with the 8 bits snugly nestled in a byte? Drumroll, please! 🥁 It’s a whopping 256 different values! That’s right, from 00000000 to 11111111, the possibilities are endless.

Comparison with Other Data Representation Systems

Comparison with decimal and hexadecimal systems.

Let’s shake things up a bit by comparing our trusty 8-bit byte with other data representation systems like decimal and hexadecimal. While decimal uses 10 digits (0-9) and hexadecimal employs 16 characters (0-9, A-F), our byte stands strong with its compact yet powerful 8-bit structure.

Advantages and Disadvantages of Using 8 Bits in a Byte for Data Representation

Ah, the age-old debate of pros and cons! The 8-bit byte offers a balance between efficiency and complexity. It’s great for representing a wide range of values efficiently, but it might fall short when handling large datasets that require more precision.

Applications of Data Representation with 8 Bits in a Byte

Use of 8 bits in a byte in computer systems.

From processing instructions to storing images and text, the humble 8-bit byte plays a crucial role in the inner workings of computer systems. It’s like the unsung hero silently powering our digital world behind the scenes.

Impact of Data Representation on Computer Processing and Storage

Imagine a world without efficient data representation—chaos, right? By optimizing how data is represented using 8 bits in a byte, we can enhance computer processing speed, reduce storage requirements, and pave the way for smarter technologies.

Overall, understanding the basics of bits and bytes opens up a treasure trove of possibilities in the vast landscape of computing. So, embrace the binary charm, dive into the world of data representation, and remember: when it doubt, byte it out! 💻✨

Random Fact: Did you know that the term “byte” was coined by Dr. Werner Buchholz in 1956 while working on the IBM Stretch computer? 🤯

In closing, keep coding, keep exploring, and may the bits be ever in your favor! 🚀

Program Code – Understanding Bits and Bytes: Exploring Data Representation

Code output:, code explanation:.

This program is all about working with the inner bits and bytes, the OG Morse code of computing if y’know what I mean. So grab your coder goggles; it’s about to get bit-y.

First, we’ve got to_binary() . This bad boy takes an integer and spits out a binary string so neat you could tie it with a bow. You can even set the number of bits for extra fun.

Next on deck is to_hex() . Ever need to cook up an integer in hex form with that chef’s kiss ‘0x’ garnish? This function has got your back.

If you’re drowning in a sea of binary with binary_to_int() , this lifeboat turns that ‘101010’ SOS into a cozy integer island you can land on.

But wait, there’s more! hex_to_int() is like your hex translator, turning those wacky ‘0x’ phrases into plain old integers you can understand.

Let’s talk text messages—old school style with ascii_to_binary() . Give it a string and bam, you have a binary sequence that practically telegraphs your message.

And if you ever need to decode those binary smoke signals back into text, binary_to_ascii() is the rescue chopper bringing you back to civilization aka ASCII land.

The main event is all about showing off these functions like proud parents at a school play. We’ve got number play, binary banter, hex chit-chat, and even a lovely ASCII-bian dramatization.

So in a nutshell, this code is the ultimate translator, bridging the gap between human-friendly and computer-lingo. Creating this and trying to explain it feels like teaching your grandma to Snapchat… but hey, I hope y’all find it as nifty as a new Spotify playlist! Thanks for tuning in, and keep on coding in the free world! ✌️👩‍💻

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Data Representation 5.3. Numbers

Data representation.

• 5.1. What's the big picture?
• 5.2. Getting started

Understanding the base 10 number system

Representing whole numbers in binary, shorthand for binary numbers - hexadecimal, computers representing numbers in practice, how many bits are used in practice, representing negative numbers in practice.

• 5.5. Images and Colours
• 5.6. Program Instructions
• 5.7. The whole story!
• 5.8. Further reading

In this section, we will look at how computers represent numbers. To begin with, we'll revise how the base 10 number system that we use every day works, and then look at binary , which is base 2. After that, we'll look at some other charactertistics of numbers that computers must deal with, such as negative numbers and numbers with decimal points.

The number system that humans normally use is in base 10 (also known as decimal). It's worth revising quickly, because binary numbers use the same ideas as decimal numbers, just with fewer digits!

In decimal, the value of each digit in a number depends on its place in the number. For example, in $123, the 3 represents $3, whereas the 1 represents $100. Each place value in a number is worth 10 times more than the place value to its right, i.e. there are the "ones", the "tens", the "hundreds", the "thousands" the "ten thousands", the "hundred thousands", the "millions", and so on. Also, there are 10 different digits (0,1,2,3,4,5,6,7,8,9) that can be at each of those place values.

If you were only able to use one digit to represent a number, then the largest number would be 9. After that, you need a second digit, which goes to the left, giving you the next ten numbers (10, 11, 12... 19). It's because we have 10 digits that each one is worth 10 times as much as the one to its right.

You may have encountered different ways of expressing numbers using "expanded form". For example, if you want to write the number 90328 in expanded form you might have written it as:

A more sophisticated way of writing it is:

If you've learnt about exponents, you could write it as:

The key ideas to notice from this are:

• Decimal has 10 digits – 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
• A place is the place in the number that a digit is, i.e. ones, tens, hundreds, thousands, and so on. For example, in the number 90328, 3 is in the "hundreds" place, 2 is in the "tens" place, and 9 is in the "ten thousands" place.
• Numbers are made with a sequence of digits.
• The right-most digit is the one that's worth the least (in the "ones" place).
• The left-most digit is the one that's worth the most.
• Because we have 10 digits, the digit at each place is worth 10 times as much as the one immediately to the right of it.

All this probably sounds really obvious, but it is worth thinking about consciously, because binary numbers have the same properties.

As discussed earlier, computers can only store information using bits, which have 2 possible states. This means that they cannot represent base 10 numbers using digits 0 to 9, the way we write down numbers in decimal. Instead, they must represent numbers using just 2 digits – 0 and 1.

Binary works in a very similar way to decimal, even though it might not initially seem that way. Because there are only 2 digits, this means that each digit is 2 times the value of the one immediately to the right.

The base 10 (decimal) system is sometimes called denary, which is more consistent with the name binary for the base 2 system. The word "denary" also refers to the Roman denarius coin, which was worth ten asses (an "as" was a copper or bronze coin). The term "denary" seems to be used mainly in the UK; in the US, Australia and New Zealand the term "decimal" is more common.

The interactive below illustrates how this binary number system represents numbers. Have a play around with it to see what patterns you can see.

Base Calculator

Find the representations of 4, 7, 12, and 57 using the interactive.

What is the largest number you can make with the interactive? What is the smallest? Is there any integer value in between the biggest and the smallest that you can’t make? Are there any numbers with more than one representation? Why/ why not?

• 000000 in binary, 0 in decimal is the smallest number.
• 111111 in binary, 63 in decimal is the largest number.
• All the integer values (0, 1, 2... 63) in the range can be represented (and there is a unique representation for each one). This is exactly the same as decimal!

You have probably noticed from the interactive that when set to 1, the leftmost bit (the "most significant bit") adds 32 to the total, the next adds 16, and then the rest add 8, 4, 2, and 1 respectively. When set to 0, a bit does not add anything to the total. So the idea is to make numbers by adding some or all of 32, 16, 8, 4, 2, and 1 together, and each of those numbers can only be included once.

Choose a number less than 61 (perhaps your house number, your age, a friend's age, or the day of the month you were born on), set all the binary digits to zero, and then start with the left-most digit (32), trying out if it should be zero or one. See if you can find a method for converting the number without too much trial and error. Try different numbers until you find a quick way of doing this.

Figure out the binary representation for 23 without using the interactive? What about 4, 0, and 32? Check all your answers using the interactive to verify they are correct.

Can you figure out a systematic approach to counting in binary? i.e. start with the number 0, then increment it to 1, then 2, then 3, and so on, all the way up to the highest number that can be made with the 7 bits. Try counting from 0 to 16, and see if you can detect a pattern. Hint: Think about how you add 1 to a number in base 10. e.g. how do you work out 7 + 1, 38 + 1, 19 + 1, 99 + 1, 230899999 + 1, etc? Can you apply that same idea to binary?

Using your new knowledge of the binary number system, can you figure out a way to count to higher than 10 using your 10 fingers? What is the highest number you can represent using your 10 fingers? What if you included your 10 toes as well (so you have 20 fingers and toes to count with).

A binary number can be incremented by starting at the right and flipping all consecutive bits until a 1 comes up (which will be on the very first bit half of the time).

Counting on fingers in binary means that you can count to 31 on 5 fingers, and 1023 on 10 fingers. There are a number of videos on YouTube of people counting in binary on their fingers. One twist is to wear white gloves with the numbers 16, 8, 4, 2, 1 on the 5 fingers respectively, which makes it easy to work out the value of having certain fingers raised.

The interactive used exactly 6 bits. In practice, we can use as many or as few bits as we need, just like we do with decimal. For example, with 5 bits, the place values would be 16, 8, 4, 2 and 1, so the largest value is 11111 in binary, or 31 in decimal. Representing 14 with 5 bits would give 01110.

Write representations for the following. If it is not possible to do the representation, put "Impossible".

• Represent 101 with 7 bits
• Represent 28 with 10 bits
• Represent 7 with 3 bits
• Represent 18 with 4 bits
• Represent 28232 with 16 bits

The answers are (spaces are added to make the answers easier to read, but are not required).

• 101 with 7 bits is: 110 0101
• 28 with 10 bits is: 00 0001 1100
• 7 with 3 bits is: 111
• 18 with 4 bits is: Impossible (not enough bits to represent value)
• 28232 with 16 bits is: 0110 1110 0100 1000

An important concept with binary numbers is the range of values that can be represented using a given number of bits. When we have 8 bits the binary numbers start to get useful – they can represent values from 0 to 255, so it is enough to store someone's age, the day of the month, and so on.

Groups of 8 bits are so useful that they have their own name: a byte . Computer memory and disk space are usually divided up into bytes, and bigger values are stored using more than one byte. For example, two bytes (16 bits) are enough to store numbers from 0 to 65,535. Four bytes (32 bits) can store numbers up to 4,294,967,295. You can check these numbers by working out the place values of the bits. Every bit that's added will double the range of the number.

In practice, computers store numbers with either 16, 32, or 64 bits. This is because these are full numbers of bytes (a byte is 8 bits), and makes it easier for computers to know where each number starts and stops.

Candles on birthday cakes use the base 1 numbering system, where each place is worth 1 more than the one to its right. For example, the number 3 is 111, and 10 is 1111111111. This can cause problems as you get older – if you've ever seen a cake with 100 candles on it, you'll be aware that it's a serious fire hazard.

Luckily it's possible to use binary notation for birthday candles – each candle is either lit or not lit. For example, if you are 18, the binary notation is 10010, and you need 5 candles (with only two of them lit).

There's a video on using binary notation for counting up to 1023 on your hands, as well as using it for birthday cakes .

Most of the time binary numbers are stored electronically, and we don't need to worry about making sense of them. But sometimes it's useful to be able to write down and share numbers, such as the unique identifier assigned to each digital device (MAC address), or the colours specified in an HTML page.

Writing out long binary numbers is tedious – for example, suppose you need to copy down the 16-bit number 0101001110010001. A widely used shortcut is to break the number up into 4-bit groups (in this case, 0101 0011 1001 0001), and then write down the digit that each group represents (giving 5391). There's just one small problem: each group of 4 bits can go up to 1111, which is 15, and the digits only go up to 9.

The solution is simple: we introduce symbols for the digits from 1010 (10) to 1111 (15), which are just the letters A to F. So, for example, the 16-bit binary number 1011 1000 1110 0001 can be written more concisely as B8E1. The "B" represents the binary 1011, which is the decimal number 11, and the E represents binary 1110, which is decimal 14.

Because we now have 16 digits, this representation is base 16, and known as hexadecimal (or hex for short). Converting between binary and hexadecimal is very simple, and that's why hexadecimal is a very common way of writing down large binary numbers.

Here's a full table of all the 4-bit numbers and their hexadecimal digit equivalent:

For example, the largest 8-bit binary number is 11111111. This can be written as FF in hexadecimal. Both of those representations mean 255 in our conventional decimal system (you can check that by converting the binary number to decimal).

Which notation you use will depend on the situation; binary numbers represent what is actually stored, but can be confusing to read and write; hexadecimal numbers are a good shorthand of the binary; and decimal numbers are used if you're trying to understand the meaning of the number or doing normal math. All three are widely used in computer science.

It is important to remember though, that computers only represent numbers using binary. They cannot represent numbers directly in decimal or hexadecimal.

A common place that numbers are stored on computers is in spreadsheets or databases. These can be entered either through a spreadsheet program or database program, through a program you or somebody else wrote, or through additional hardware such as sensors, collecting data such as temperatures, air pressure, or ground shaking.

Some of the things that we might think of as numbers, such as the telephone number (03) 555-1234, aren't actually stored as numbers, as they contain important characters (like dashes and spaces) as well as the leading 0 which would be lost if it was stored as a number (the above number would come out as 35551234, which isn't quite right). These are stored as text , which is discussed in the next section.

On the other hand, things that don't look like a number (such as "30 January 2014") are often stored using a value that is converted to a format that is meaningful to the reader (try typing two dates into Excel, and then subtract one from the other – the result is a useful number). In the underlying representation, a number is used. Program code is used to translate the underlying representation into a meaningful date on the user interface.

The difference between two dates in Excel is the number of days between them; the date itself (as in many systems) is stored as the amount of time elapsed since a fixed date (such as 1 January 1900). You can test this by typing a date like "1 January 1850" – chances are that it won't be formatted as a normal date. Likewise, a date sufficiently in the future may behave strangely due to the limited number of bits available to store the date.

Numbers are used to store things as diverse as dates, student marks, prices, statistics, scientific readings, sizes and dimensions of graphics.

The following issues need to be considered when storing numbers on a computer:

• What range of numbers should be able to be represented?
• How do we handle negative numbers?
• How do we handle decimal points or fractions?

In practice, we need to allocate a fixed number of bits to a number, before we know how big the number is. This is often 32 bits or 64 bits, although can be set to 16 bits, or even 128 bits, if needed. This is because a computer has no way of knowing where a number starts and ends, otherwise.

Any system that stores numbers needs to make a compromise between the number of bits allocated to store the number, and the range of values that can be stored.

In some systems (like the Java and C programming languages and databases) it's possible to specify how accurately numbers should be stored; in others it is fixed in advance (such as in spreadsheets).

Some are able to work with arbitrarily large numbers by increasing the space used to store them as necessary (e.g. integers in the Python programming language). However, it is likely that these are still working with a multiple of 32 bits (e.g. 64 bits, 96 bits, 128 bits, 160 bits, etc). Once the number is too big to fit in 32 bits, the computer would reallocate it to have up to 64 bits.

In some programming languages there isn't a check for when a number gets too big (overflows). For example, if you have an 8-bit number using two's complement, then 01111111 is the largest number (127), and if you add one without checking, it will change to 10000000, which happens to be the number -128. (Don't worry about two's complement too much, it's covered later in this section.) This can cause serious problems if not checked for, and is behind a variant of the Y2K problem, called the Year 2038 problem , involving a 32-bit number overflowing for dates on Tuesday, 19 January 2038.

On tiny computers, such as those embedded inside your car, washing machine, or a tiny sensor that is barely larger than a grain of sand, we might need to specify more precisely how big a number needs to be. While computers prefer to work with chunks of 32 bits, we could write a program (as an example for an earthquake sensor) that knows the first 7 bits are the lattitude, the next 7 bits are the longitude, the next 10 bits are the depth, and the last 8 bits are the amount of force.

Even on standard computers, it is important to think carefully about the number of bits you will need. For example, if you have a field in your database that could be either "0", "1", "2", or "3" (perhaps representing the four bases that can occur in a DNA sequence), and you used a 64 bit number for every one, that will add up as your database grows. If you have 10,000,000 items in your database, you will have wasted 62 bits for each one (only 2 bits is needed to represent the 4 numbers in the example), a total of 620,000,000 bits, which is around 74 MB. If you are doing this a lot in your database, that will really add up – human DNA has about 3 billion base pairs in it, so it's incredibly wasteful to use more than 2 bits for each one.

And for applications such as Google Maps, which are storing an astronomical amount of data, wasting space is not an option at all!

It is really useful to know roughly how many bits you will need to represent a certain value. Have a think about the following scenarios, and choose the best number of bits out of the options given. You want to ensure that the largest possible number will fit within the number of bits, but you also want to ensure that you are not wasting space.

• Storing the day of the week - a) 1 bit - b) 4 bits - c) 8 bits - d) 32 bits
• Storing the number of people in the world - a) 16 bits - b) 32 bits - c) 64 bits - d) 128 bits
• Storing the number of roads in New Zealand - a) 16 bits - b) 32 bits - c) 64 bits - d) 128 bits
• Storing the number of stars in the universe - a) 16 bits - b) 32 bits - c) 64 bits - d) 128 bits
• b (actually, 3 bits is enough as it gives 8 values, but amounts that fit evenly into 8-bit bytes are easier to work with)
• c (32 bits is slightly too small, so you will need 64 bits)
• b (This is a challenging question, but one a database designer would have to think about. There's about 94,000 km of roads in New Zealand, so if the average length of a road was 1km, there would be too many roads for 16 bits. Either way, 32 bits would be a safe bet.)
• d (Even 64 bits is not enough, but 128 bits is plenty! Remember that 128 bits isn't twice the range of 64 bits.)

The binary number representation we have looked at so far allows us to represent positive numbers only. In practice, we will want to be able to represent negative numbers as well, such as when the balance of an account goes to a negative amount, or the temperature falls below zero. In our normal representation of base 10 numbers, we represent negative numbers by putting a minus sign in front of the number. But in binary, is it this simple?

We will look at two possible approaches: Adding a simple sign bit, much like we do for decimal, and then a more useful system called two's complement.

Using a simple sign bit

On a computer we don’t have minus signs for numbers (it doesn't work very well to use the text based one when representing a number because you can't do arithmetic on characters), but we can do it by allocating one extra bit, called a sign bit, to represent the minus sign. Just like with decimal numbers, we put the negative indicator on the left of the number — when the sign bit is set to "0", that means the number is positive and when the sign bit is set to "1", the number is negative (just as if there were a minus sign in front of it).

For example, if we wanted to represent the number 41 using 7 bits along with an additional bit that is the sign bit (to give a total of 8 bits), we would represent it by 00101001 . The first bit is a 0, meaning the number is positive, then the remaining 7 bits give 41 , meaning the number is +41 . If we wanted to make -59 , this would be 10111011 . The first bit is a 1, meaning the number is negative, and then the remaining 7 bits represent 59 , meaning the number is -59 .

Using 8 bits as described above (one for the sign, and 7 for the actual number), what would be the binary representations for 1, -1, -8, 34, -37, -88, and 102?

The spaces are not necessary, but are added to make reading the binary numbers easier

• 1 is 0000 0001
• -1 is 1000 0001
• -8 is 1000 1000
• 34 is 0010 0010
• -37 is 1010 0101
• -88 is 1101 1000
• 102 is 0110 0110

Going the other way is just as easy. If we have the binary number 10010111 , we know it is negative because the first digit is a 1. The number part is the next 7 bits 0010111 , which is 23 . This means the number is -23 .

What would the decimal values be for the following, assuming that the first bit is a sign bit?

• 00010011 is 19
• 10000110 is -6
• 10100011 is -35
• 01111111 is 127
• 11111111 is -127

But what about 10000000? That converts to -0 . And 00000000 is +0 . Since -0 and +0 are both just 0, it is very strange to have two different representations for the same number.

This is one of the reasons that we don't use a simple sign bit in practice. Instead, computers usually use a more sophisticated representation for negative binary numbers called two's complement .

Two's complement

There's an alternative representation called two's complement , which avoids having two representations for 0, and more importantly, makes it easier to do arithmetic with negative numbers.

Representing positive numbers with two's complement

Representing positive numbers is the same as the method you have already learnt. Using 8 bits ,the leftmost bit is a zero and the other 7 bits are the usual binary representation of the number; for example, 1 would be 00000001 , and 50 would be 00110010 .

Representing negative numbers with two's complement

This is where things get more interesting. In order to convert a negative number to its two's complement representation, use the following process. 1. Convert the number to binary (don't use a sign bit, and pretend it is a positive number). 2. Invert all the digits (i.e. change 0's to 1's and 1's to 0's). 3. Add 1 to the result (Adding 1 is easy in binary; you could do it by converting to decimal first, but think carefully about what happens when a binary number is incremented by 1 by trying a few; there are more hints in the panel below).

For example, assume we want to convert -118 to its two's complement representation. We would use the process as follows. 1. The binary number for 118 is 01110110 . 2. 01110110 with the digits inverted is 10001001 . 3. 10001001 + 1 is 10001010 .

Therefore, the two's complement representation for -118 is 10001010 .

The rule for adding one to a binary number is pretty simple, so we'll let you figure it out for yourself. First, if a binary number ends with a 0 (e.g. 1101010), how would the number change if you replace the last 0 with a 1? Now, if it ends with 01, how much would it increase if you change the 01 to 10? What about ending with 011? 011111?

The method for adding is so simple that it's easy to build computer hardware to do it very quickly.

What would be the two's complement representation for the following numbers, using 8 bits ? Follow the process given in this section, and remember that you do not need to do anything special for positive numbers.

• 19 in binary is 0001 0011 , which is the two's complement for a positive number.
• For -19, we take the binary of the positive, which is 0001 0011 (above), invert it to 1110 1100, and add 1, giving a representation of 1110 1101 .
• 107 in binary is 0110 1011 , which is the two's complement for a positive number.
• For -107, we take the binary of the positive, which is 0110 1011 (above), invert it to 1001 0100, and add 1, giving a representation of 1001 0101 .
• For -92, we take the binary of the positive, which is 0101 1100, invert it to 1010 0011, and add 1, giving a representation of 1010 0100 . (If you have this incorrect, double check that you incremented by 1 correctly).

Converting a two's complement number back to decimal

In order to reverse the process, we need to know whether the number we are looking at is positive or negative. For positive numbers, we can simply convert the binary number back to decimal. But for negative numbers, we first need to convert it back to a normal binary number.

So how do we know if the number is positive or negative? It turns out (for reasons you will understand later in this section) that two's complement numbers that are negative always start in a 1, and positive numbers always start in a 0. Have a look back at the previous examples to double check this.

So, if the number starts with a 1, use the following process to convert the number back to a negative decimal number.

• Subtract 1 from the number.
• Invert all the digits.
• Convert the resulting binary number to decimal.
• Add a minus sign in front of it.

So if we needed to convert 11100010 back to decimal, we would do the following.

• Subtract 1 from 11100010 , giving 11100001 .
• Invert all the digits, giving 00011110 .
• Convert 00011110 to a binary number, giving 30 .
• Add a negative sign, giving -30 .

Convert the following two's complement numbers to decimal.

• 10001100 -> (-1) 10001011 -> (inverted) 01110100 -> (to decimal) 116 -> (negative sign added) -116
• 10111111 -> (-1) 10111110 -> (inverted) 01000001 -> (to decimal) 65 -> (negative sign added) -65

How many numbers can be represented using two's complement?

While it might initially seem that there is no bit allocated as the sign bit, the left-most bit behaves like one. With 8 bits, you can still only make 256 possible patterns of 0's and 1's. If you attempted to use 8 bits to represent positive numbers up to 255, and negative numbers down to -255, you would quickly realise that some numbers were mapped onto the same pattern of bits. Obviously, this will make it impossible to know what number is actually being represented!

In practice, numbers within the following ranges can be represented. Unsigned Range is how many numbers you can represent if you only allow positive numbers (no sign is needed), and two's complement Range is how many numbers you can represent if you require both positive and negative numbers. You can work these out because the range of 8-bit values if they are stored using unsigned numbers will be from 00000000 to 11111111 (i.e. 0 to 255 in decimal), while the signed two's complement range is from 10000000 (the lowest number, -128 in decimal) to 01111111 (the highest number, 127 in decimal). This might seem a bit weird, but it works out really well because normal binary addition can be used if you use this representation even if you're adding a negative number.

Adding negative binary numbers

Before adding negative binary numbers, we'll look at adding positive numbers. It's basically the same as the addition methods used on decimal numbers, except the rules are way simpler because there are only two different digits that you might add!

You've probably learnt about column addition. For example, the following column addition would be used to do 128 + 255 .

When you go to add 5 + 8, the result is higher than 9, so you put the 3 in the one's column, and carry the 1 to the 10's column. Binary addition works in exactly the same way.

Adding positive binary numbers

If you wanted to add two positive binary numbers, such as 00001111 and 11001110 , you would follow a similar process to the column addition. You only need to know 0+0, 0+1, 1+0, and 1+1, and 1+1+1. The first three are just what you might expect. Adding 1+1 causes a carry digit, since in binary 1+1 = 10, which translates to "0, carry 1" when doing column addition. The last one, 1+1+1 adds up to 11 in binary, which we can express as "1, carry 1". For our two example numbers, the addition works like this:

Remember that the digits can be only 1 or 0. So you will need to carry a 1 to the next column if the total you get for a column is (decimal) 2 or 3.

Adding negative numbers with a simple sign bit

With negative numbers using sign bits like we did before, this does not work. If you wanted to add +11 (01011) and -7 (10111) , you would expect to get an answer of +4 (00100) .

Which is -2 .

One way we could solve the problem is to use column subtraction instead. But this would require giving the computer a hardware circuit which could do this. Luckily this is unnecessary, because addition with negative numbers works automatically using two's complement!

Adding negative numbers with two's complement

For the above addition (+11 + -7), we can start by converting the numbers to their 5-bit two's complement form. Because 01011 (+11) is a positive number, it does not need to be changed. But for the negative number, 00111 (-7) (sign bit from before removed as we don't use it for two's complement), we need to invert the digits and then add 1, giving 11001 .

Adding these two numbers works like this:

Any extra bits to the left (beyond what we are using, in this case 5 bits) have been truncated. This leaves 00100 , which is 4 , like we were expecting.

We can also use this for subtraction. If we are subtracting a positive number from a positive number, we would need to convert the number we are subtracting to a negative number. Then we should add the two numbers. This is the same as for decimal numbers, for example 5 - 2 = 3 is the same as 5 + (-2) = 3.

This property of two's complement is very useful. It means that positive numbers and negative numbers can be handled by the same computer circuit, and addition and subtraction can be treated as the same operation.

The idea of using a "complementary" number to change subtraction to addition can be seen by doing the same in decimal. The complement of a decimal digit is the digit that adds up to 10; for example, the complement of 4 is 6, and the complement of 8 is 2. (The word "complement" comes from the root "complete" – it completes it to a nice round number.)

Subtracting 2 from 6 is the same as adding the complement, and ignoring the extra 1 digit on the left. The complement of 2 is 8, so we add 8 to 6, giving (1)4.

For larger numbers (such as subtracting the two 3-digit numbers 255 - 128), the complement is the number that adds up to the next power of 10 i.e. 1000-128 = 872. Check that adding 872 to 255 produces (almost) the same result as subtracting 128.

Working out complements in binary is way easier because there are only two digits to work with, but working them out in decimal may help you to understand what is going on.

Using sign bits vs using two's complement

We have now looked at two different ways of representing negative numbers on a computer. In practice, a simple sign bit is rarely used, because of having two different representations of zero, and requiring a different computer circuit to handle negative and positive numbers, and to do addition and subtraction.

Two's complement is widely used, because it only has one representation for zero, and it allows positive numbers and negative numbers to be treated in the same way, and addition and subtraction to be treated as one operation.

There are other systems such as "One's Complement" and "Excess-k", but two's complement is by far the most widely used in practice.

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What is Bit?

Bit have high importance in computer memory, networks because computer understand the things, codes even multimedia in form of bits. Not in the language we communicate How do they communicate with each other and with us? How do they represent text, images, sounds, and videos? The answer to all these questions lies in the concept of a bit, the most basic unit of information in computing and digital communications.

What is a Bit?

Bits stand for Binary Digit. Where binary means two things or two elements. Digit means a symbol which represents a number. So, bit consists two symbols in form of numbers which are 0 and 1. We call these values as Binary states, which simply represent yes or no, true or false like 0 for true and 1 for false etc. They store all the information or data in form of 0 and 1. This is binary number system which computer is using

Binary System

In real life, we use decimal system which consists 0 to 9 digits in the same way binary system uses two digits 0 and 1. All the information whether its text image or multimedia is represented in form of bits Lets take a overview how data is stored in form of bits

Represent Text in Bit

1. using ascii.

We can represent Text in binary form using ASCII (American Standard Code for Information Interchange). It represents binary number in form of bytes. Collection of 8 bits make a byte. ASCII provides a unique 7 digit code in binary form which represent letters. Like for example

You can get the values of text in binary format using ASCII Table

• H is represented as 72 in decimal, which is 1001000 in binary (7 bits).
• E is represented as 69 in decimal, which is 1000101 in binary (7 bits).
• L is represented as 76 in decimal, which is 1001100 in binary (7 bits).
• O is represented as 79 in decimal, which is 1001111 in binary (7 bits).

So, the word “HELLO” in binary ASCII representation is: 1001000 1000101 1001100 1001100 1001111.

2. Using Unicode

Unicode means single code, it assigns a code point to every character or symbol in the world so its a hexadecimal code For example if we need to convert “HELLO” to binary using unicode

First, we need to find the code points of each letter in the word “hello”. We can use a Unicode table to do this The code points of “hello” are:

h in unicode is written represented as = U+0068 e in unicode is written represented as = U+0065 l in unicode is written represented as= U+006C o in unicode is written represented as = U+006F

These codes can be converted to binary using hexadecimal to binary converter because computer can understand binary language

h in binary = 0000 0110 1000 e in binary = 0000 0110 0101 l in binary = 0000 0110 1100 o in binary = 0000 0110 1111

UTF-8 encoding rules

For the code point between range of U+0000 and U+007F, use one byte and prefix it with a zero.

For the code point between range of U+0080 and U+07FF, use two bytes and prefix them with 110 and 10 respectively.

For the code point between range of U+0800 and U+FFFF, use three bytes and prefix them with 1110 and 10 respectively.

For the code point between range of U+10000 and U+10FFFF, use four bytes and prefix them with 11110 and 10 respectively.

Since all the code points of “hello” are between U+0000 and U+007F, we only need one byte for each letter, and we prefix them with a zero. The UTF-8 encoded bytes of “hello” are:

h = 0110 1000 e = 0110 0101 l = 0110 1100 o = 0110 1111

Finally, we concatenate these bytes to form the UTF-8 encoded word “hello”. The result is:

hello = 01101000 01100101 01101100 01101100 01101111

Represent Image in Bit

The basic idea of representing image is to divide the image in form of small pixels assign a binary code to all different pixels on basis of its color and brightness. The more the size of image means that more number of colors, shades are used in image.

For example if we have to represent an image in BMP format. which is stored as a matrix of pixels, each pixel having a fixed number of bits to represent its color. Like, a 2×2 pixel image with black and white colors can be encoded as 00000000 00000000 11111111 11111111 in BMP. Here each pixel represents (8bit) so we have got this code of 8 digit. The first pair of bytes represents the top-left pixel, which is black (00000000 00000000), the second pair represents the top-right pixel, which is white (11111111 11111111), and so on

Properties of Bit

• Bit is smallest unit of digital data which contains only two values 0 and 1
• Every bit is independent in itself and carries different data, changing 1 bit will not affect the data of other bit
• In boolean algebra, where there are only two values (true and false, true is represented by 1 and 0 is for false)
• If two bits are complement of each other like one is 0 and other is 1 then they form dual relationship.
• The higher number of bit used, the more data can be stored so accuracy of data is determined by how many bits are used like 8 Bit 16 bit or 32 bit

Uses of Bit

• Data Representation: Bit are the most basic and fundamental data of storing and representing data in different formats. It can encode text, images, video and audio file
• Computer Processing: As we know computers operate in Binary language and can understand language of 0 and 1 . CPUs (Central Processing Units) manipulate bits to process data, run software, and perform various tasks.
• Error Detection and Correction : In data communication , bits are used for error detection and correction. Techniques like checksums and error-correcting codes help ensure data integrity.
• Character Encoding: For representation of text bits use encoding techniques such as ACII, Unicode etc. This is important for communication between machine and human.
• Security: Bits are very important for encryption and security protocols. Cryptographic algorithms, such as XOR (exclusive OR), use bitwise operations to manipulate data at the bit level.
• Compression: Bits are essential for compression of data. Compression means reducing the size of data by removing unimportant information from bits. It is done is multimedia
• Control System s: In digital control systems, bits are used to encode commands and states, allowing for the automation of various processes and systems.

FAQs on What is Bit?

Q.1: what is difference between similar terms bit and byte.

Bit is the smallest unit of data, it can have 2 values 0 or 1. While byte is made up of 8 bits so it can store more data ex. byte can store value between 0 to 255

Q.2: Write commonly used units which are formed by combining bits?

There are many units like kilobit, megabit, gigabit, terabit etc.

Q.3: What are Qubits?

Here we can understand from name ‘Qu’ represent quantum and bits. So the bits used in quantum computing are known as qubits. Qubits can store superposition of both binary digits 0 and 1 at the same time.

Q.4: What does the term ‘bit rate ‘ stands for?

Its the rate at which bits are transmitted or processed per unit of time, typically measured in bits per second (bps).

Q.5: Why bits are important in computing?

Bits are useful for storing and processing different types of data whether its text, image or digital information.

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ARCHIVED: What are bits, bytes, and other units of measure for digital information?

Note: The following information is provided in part by the Extreme Science and Engineering Discovery Environment ( XSEDE ), a National Science Foundation ( NSF ) project that provides researchers with advanced digital resources and services that facilitate scientific discovery. For more, see the XSEDE website .

A bit is a binary digit, the smallest increment of data on a computer. A bit can hold only one of two values: 0 or 1, corresponding to the electrical values of off or on, respectively.

Because bits are so small, you rarely work with information one bit at a time. Bits are usually assembled into a group of eight to form a byte . A byte contains enough information to store a single ASCII character, like "h".

A kilobyte (KB) is 1,024 bytes, not one thousand bytes as might be expected, because computers use binary (base two) math, instead of a decimal (base ten) system.

Computer storage and memory is often measured in megabytes (MB) and gigabytes (GB). A medium-sized novel contains about 1 MB of information. 1 MB is 1,024 kilobytes, or 1,048,576 (1024x1024) bytes, not one million bytes.

Similarly, one 1 GB is 1,024 MB, or 1,073,741,824 (1024x1024x1024) bytes. A terabyte (TB) is 1,024 GB; 1 TB is about the same amount of information as all of the books in a large library, or roughly 1,610 CDs worth of data. A petabyte (PB) is 1,024 TB. 1 PB of data, if written on DVDs, would create roughly 223,100 DVDs, i.e., a stack about 878 feet tall, or a stack of CDs a mile high. Indiana University is now building storage systems capable of holding petabytes of data. An exabyte (EB) is 1,024 PB. A zettabyte (ZB) is 1,024 EB. Finally, a yottabyte (YB) is 1,024 ZB.

Many hard drive manufacturers use a decimal number system to define amounts of storage space. As a result, 1 MB is defined as one million bytes, 1 GB is defined as one billion bytes, and so on. Since your computer uses a binary system as mentioned above, you may notice a discrepancy between your hard drive's published capacity and the capacity acknowledged by your computer. For example, a hard drive that is said to contain 10 GB of storage space using a decimal system is actually capable of storing 10,000,000,000 bytes. However, in a binary system, 10 GB is 10,737,418,240 bytes. As a result, instead of acknowledging 10 GB, your computer will acknowledge 9.31 GB. This is not a malfunction but a matter of different definitions.

We count in base 10 by powers of 10:

Computers count by base 2:

So in computer jargon, the following units are used:

Note: The names and abbreviations for numbers of bytes are easily confused with the notations for bits. The abbreviations for numbers of bits use a lower-case "b" instead of an upper-case "B". Since one byte is made up of eight bits, this difference can be significant. For example, if a broadband Internet connection is advertised with a download speed of 3.0 M b ps, its speed is 3.0 mega bits per second, or 0.375 mega bytes per second (which would be abbreviated as 0.375 M B ps). Bits and bit rates (bits over time, as in bits per second [bps]) are most commonly used to describe connection speeds, so pay particular attention when comparing Internet connection providers and services.

This document was developed with support from National Science Foundation ( NSF ) grants 1053575 and 1548562 . Any opinions, findings, conclusions, or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the NSF.

This is document ackw in the Knowledge Base. Last modified on 2018-01-18 10:52:24 .

Data Representation in Computer: Number Systems, Characters, Audio, Image and Video

What is data representation in computer.

Before discussing data representation of numbers, let us see what a number system is.

Number Systems

Binary number system.

A Binary number system has only two digits that are 0 and 1. Every number (value) represents 0 and 1 in this number system. The base of the binary number system is 2 because it has only two digits.

Octal Number System

Decimal number system, hexadecimal number system, data representation of characters.

The code called ASCII (pronounced ‘􀀏’.S-key”), which stands for American Standard Code for Information Interchange, uses 7 bits to represent each character in computer memory. The ASCII representation has been adopted as a standard by the U.S. government and is widely accepted.

Using 8-bit ASCII we can represent only 256 characters. This cannot represent all characters of written languages of the world and other symbols. Unicode is developed to resolve this problem. It aims to provide a standard character encoding scheme, which is universal and efficient.

Data Representation of Audio, Image and Video

In most cases, we may have to represent and process data other than numbers and characters. This may include audio data, images, and videos. We can see that like numbers and characters, the audio, image, and video data also carry information.

FAQs About Data Representation in Computer

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Computer Concepts : Bits, Bytes and Words

In Computers; Bits, Bytes & Words are the core concepts.

Bits – binary digits

Computer memory stores the data in bits. Each bit stores the value either 0 or 1. Inside the Computer, there are electronic switches that store the bit values; either 0 or 1. If the switch is OFF means, that represents 0 & the switch is ON means, that represents 1. That means Computer can understand the data in “0”s and “1”s. We normally use bits to represent processor architecture or design; a 32-bit processor, 64-bit processor, etc. 64-bit processor can do the computations faster than a 32-bit processor.

There must be a data transfer between Computer Memory (RAM – Random Access Memory) and the Computer Processor (CPU). The data transfer happens through BUSes. Each BUS carries an N-number of bits; depending on the Computer Architecture. Each BUS has wires to transfer the bits; 16-bit BUS carries 16-bits at a time, and it has 16 wires to transfer each bit. BUSes are used to carry the information between one Component to another Component in the Computer.

Mostly, we don’t directly deal with the Computer bits; there are computer languages that allow us to directly deal with the computer bits. “C” language provides some features to allow the programmers to directly deal with the bits.

How do we represents the data other than 0 & 1; example, characters (‘A’, ‘h’ etc,.).? The answer is Byte; another term, we use in the computer terminology is Bytes.

A byte is a grouping of consecutive bits. Usually, 8-bits represents a Byte. Generally, we use Byte(s) to represent characters; each byte can store the values from 0-255. That means, we can store one of the characters from 0-255; in 1 Byte.

The most common term we use in Computers terminology is Bytes. Computer Programs read & write the Bytes from the Memory; also read and write the Bytes to the File Storage, and for the data processing use Bytes; file sizes will display in Bytes and etc.,

How internally Bytes store that data.? Simple, it is Bits. The Byte representation of a character ‘ A ‘ is:

ASCII Character value of ‘A’ is 65. Bit representation (binary representation) of ‘A’ in a Byte is below:

Note that , it is not compulsory that 8-bits are used for a Byte in all the Systems. The number of bits used for a Byte is depended on the System Architecture. Commonly we use 8-bits for a Byte.

WORDs are also consecutive bits or bytes. This term is mostly used for CPU registers. Generally, each WORD has a length of 16-bits. CPU Registers are used to store a small piece of information while doing the calculations or processing the data. These are helpful to improve the performance of the system while doing the calculation or processing.

Note that , there are Systems that use 8-bit, 32-bit, 64-bits, 128-bits for WORDs. Commonly we use 16-bits for a WORD. The number of bits used for a WORD is purely depending on the System Architecture or design.

4 thoughts on “ Computer Concepts : Bits, Bytes and Words ”

I had my first computer class over 30 years ago and I wish that the textbook, along with others, had this information in it from the beginning. I have never seen this explanation before and it makes things very understandable now. Thank You

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How are negative numbers represented in 32-bit signed integer?

How are negative number represented in 32-bit signed integer? Is it two's or one's complement? or the last bit on the left is like a flag? For example: (-10)

• 5 In what context? Different systems/platforms will do things differently. –  Michael Myers ♦ Commented May 28, 2010 at 18:41
• 2 Do you mean "first bit on the left"? –  aaaa bbbb Commented May 28, 2010 at 18:45

7 Answers 7

Most computers these days use two's complement for signed integers, but it can vary by hardware architecture, programming language, or other platform-specific issues.

For a two's-complement representation, the most-significant ("leftmost") bit is referred to as the sign bit , and it will be set for a negative integer and clear for a non-negative integer. However, it is more than just a "flag". See the Wikipedia article for more information.

• So the front bit will 1 for negative and 0 for positive? What about 0? –  User Commented Apr 13, 2015 at 16:13
• Zero is represented by all bits being zero. –  Kristopher Johnson Commented Apr 13, 2015 at 16:57

I think the answer is 0110 , preceeded by 1 repeated 28 times, therefore it looks like:

1111 1111 1111 1111 1111 1111 1111 0110;

bit representation for 10 is:

0000 0000 0000 0000 0000 0000 0000 1010;

0->1 and 1->0 for all the bits:

1111 1111 1111 1111 1111 1111 1111 0101;

add 1 to the last bit, and propagate to the bit ahead, done!

You can verify by adding it with 10, and you will get 0 for all bits. As mentioned above, it is 2-based and follows two's complement.

• clearly explained. Please can you use this method of explanation to explain how floating point numbers are stored. –  Uchenna Nwanyanwu Commented Sep 9, 2018 at 20:10

Usually it's twos-complement.

From the C99 standard:

For signed integer types, the bits of the object representation shall be divided into three groups: value bits, padding bits, and the sign bit. There need not be any padding bits; there shall be exactly one sign bit. Each bit that is a value bit shall have the same value as the same bit in the object representation of the corresponding unsigned type (if there are M value bits in the signed type and N in the unsigned type, then M = N). If the sign bit is zero, it shall not affect the resulting value. If the sign bit is one, the value shall be modified in one of the following ways: — the corresponding value with sign bit 0 is negated (sign and magnitude); — the sign bit has the value -(2N) (two’s complement); — the sign bit has the value -(2N - 1) (ones’ complement). Which of these applies is implementation-defined, as is whether the value with sign bit 1 and all value bits zero (for the first two), or with sign bit and all value bits 1 (for ones’ complement), is a trap representation or a normal value. In the case of sign and magnitude and ones’ complement, if this representation is a normal value it is called a negative zero.

& so on

The most significant bit (last bit on the left) is set for negative numbers.

• 1 Do you mean "first bit on the left"? –  aaaa bbbb Commented May 28, 2010 at 18:44
• How about "first bit FROM the left" or "Last bit FROM the right". :) –  kirk.burleson Commented May 28, 2010 at 19:14

Just for reference: negation -> adding one .

Take 5 as an example in 8 bits, quoted from wiki

There is a trick to convert a number from positive to negative or vice verse:

Adding them ignoring their signed bit (the leftmost bit) will give you 2^N (where N is the amount of the bits to represent the number).

As the example above in 8-bit representation the sum of 5 (0000 0101) and -5 (1111 1011) will give you 1 0000 0000 which is (2 ^ 8).

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The Spectrum full-size retro computer leaks — $99 device with 48 games will arrive in November

Users can load their own games via USB.

A full-sized modern remake of the classic 8-bit Sinclair ZX Spectrum computer created by Retro Games, and marketed as The Spectrum , looks set to launch shortly. Modeled on the iconic Spectrum 48K design, with rubber block keys and rainbow stripe, the new device offers 48 built-in games and makes it easy for retro enthusiasts to load their own titles via USB. The Spectrum 48K and 128K compatible machine has leaked in listings on Polish and UK online retailers, with availability from Nov 22, and has a price of £89, likely to translate to $99 at US distributors.

Retro mini consoles and home computers have been popular in recent years, and the latest trend is for full-size replicas. Retro Games launched The C64 to capitalize on retro enthusiasts wanting bigger more fully-functioned toys, and The Spectrum is going to be the next big thing. Hopefully, a follow-up to The A500 Mini will deliver a full-size Amiga replica to fans in the coming months.

Moving our focus back to The Spectrum, and though no official product pages are available from Retro Games, the packaging shots and retail listings spill most of the beans. Most importantly, this device is supposed to deliver comprehensive Spectrum fun with the convenience of modern interfaces like HDMI and USB, as well as the fully functioning replica keyboard – so you could perhaps prod in your own Sinclair BASIC games.

The Spectrum key specifications:

• IN THE BOX: The Spectrum Home Computer, USB-C Power Supply Cable (1.8m - 6ft) (AC Adapter NOT included), HDMI Cable (1.8m - 6ft).
• Emulates 48 and 128 models of the ZX Spectrum.
• Fully working replica keyboard.
• 48 games built-in, including; Manic Miner, The Hobbit, and Head Over Heels.
• Multi region 720 HD output via HDMI, with PAL (50Hz) and NTSC (60Hz) compatibility. Play in original 4:3 or pixel perfect aspect ratios, with or without CRT filters and configurable border size.
• Choose from 12 attractive frames to surround gameplay.
• Save games at any point in one of 4 slots per game and rewind gameplay by up to 40 seconds.
• Play games you own via a USB flash drive with multiple file-type compatibility (TAP/TZX/PZX/SZX/Z80/SNA).
• Four USB-A Ports to add additional controllers for multiplayer games, and for USB flash drive.

While the above specs make it clear you will have to use your own power supply, and it should be easy with a USB-C cable provided, no mention of a bundled joystick is a worry. None of the retail listings show a joystick or joypad either. This would be a sizable omission, with the primary focus of nostalgic buyers being gaming.

The built-in games list isn’t the most important thing here, as it is going to be easy to add your own via USB. However, the packaging highlights some classic built-in titles like Manic Miner, The Hobbit, Saboteur, and Head Over Heels.

Overall, the device looks good, and appears to be a comprehensive retro offering, but we would hold back for reviews looking for mentions of any audio / visual glitches, and whether a joystick/joypad is indeed bundled. Some retro-focused channels indicate the official launch will be this Tuesday, but remember that availability isn’t scheduled until Nov 22. While you wait, there are plenty of ways to enjoy Spectrum retro gaming on your PC, Raspberry Pi , tablet, smartphone, or browser. Surprisingly, there are still new games coming to the platform in 2024.

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Mark Tyson is a news editor at Tom's Hardware. He enjoys covering the full breadth of PC tech; from business and semiconductor design to products approaching the edge of reason.

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• Pierce2623 So is it pure software emulation? FPGA? A hardware clone? Well, I guess having USB rules out the last one. Reply

Pierce2623 said: So is it pure software emulation? FPGA? A hardware clone? Well, I guess having USB rules out the last one.

Findecanor said: The previous The previous products from Retro Games Ltd have all been software-emulation on ARM SoCs.

• OneMoreUser The lack of a joystick isn't a big deal. Joysticks weren't really a big thing with the ZX Spectrum, so I doubt it will be missed much. I think the lack of audio in for hooking up a cassette player and loading original games stored on cassette tapes is "more" of an issue. Also just for the record. Any PC can run a ZX Spectrum emulator, the download will take only a second or two. Reply
• View All 4 Comments

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Last year, United Talent Agency was one of the first agencies in Hollywood to achieve the Human Rights Campaign Equality 100 award as leaders in the LGBTQ workspace inclusion. Not only is it a positive environment for its queer agents, but those agents also have the autonomy in who they want to represent. “We’ve built a really great business in representing overall LGBTQ+ talent, specifically within that niche, representation for drag artists,” said agent Pranav Mandavia.

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Since then, UTA has become a trailblazing leader in representing drag artists including Monét X Change, Violet Chachki, Bob the Drag Queen, Trixie Mattel, Katya Zamolodchikova and Gottmik. And that roster is ever growing.

Mandavia was joined by his colleagues Jacob Fenton – partner and agent (TV Talent), Ugo Obioha, agent (MP Lit), Michael Grinspan, agent (Comedy Touring) and Lucinda Moorhead, partner and agent (TV Lit) to discuss the business of pride , drag and LGBTQ+ representation within UTA, but also externally.

Having been with the agency for over 24 years, Fenton has seen UTA evolve and create a comfortable, strong and supportive environment for its LGBTQ+ employees. “It’s a good business decision because it creates more opportunities for clients in that community,” he said.

Moorhead, who has been with the agency for 13 years, added the internal support ripples down to its agents and empowers them to reflect that strength in work. The community is still greatly underrepresented in many ways, but progress is being made slowly.

While Pride month is important to many brands ensuring they’re working to be allies, the agents work year-round with brands, businesses and Hollywood executives all year round. Globally, LGBTQ+ spending power sits at $3.1 trillion. Companies and brands are looking to do better with LGBTQ+ inclusion and show support for equality, and strategically explore ways of tapping into that spending power.

Grinspan fields calls to potential buyers across the country explaining the commercial value of drag shows. The spending power speaks for itself, as do ticket sales. Grinspan said, “Drag has one of the highest average ticket prices of any touring standup. The social media following of a drag queen is generally five to ten times higher than a standup who sells a similar number of tickets.”

Drag queens are also renowned for doing their makeup and hair, and many thrive in that space using their social media platforms as a place to showcase their talent. When Mandavia talks to brands, he’ll share backend analytics from social media to show the value and power of drag artists who do their glam.

However, for every brand willing to form partnerships, some are rooted in conservative values — that’s where he steps forward to educate clients. “It’s my job as an agent, as a representative of these queens or these artists, whether they’re a drag artist or just an LGBTQ+ creator to show that there’s an audience and you should be partnering with these voices because they’re prolific.”

It’s not just drag queens on their roster. Elliot Page and Mj Rodriguez are among their many LGBTQ+ clients. Fenton noted brands such as Gucci and Charlotte Tilbury have used their clients for campaigns. Page recently was one of the faces of Gucci’s fragrance. Such a partnership is essential and signals a move of the needle in the right direction of representation.

Unfortunately, certain states aren’t as progressive and have been pushing forward anti-LGBTQ+ legislation. Obioha points out that this has negatively impacted LGBTQ+. representation in entertainment. But despite that, production houses are pushing back to counter that narrative. “Many of these production houses are led by LGBTQ+ creators. So I do think that there has been an increase and a trend to push for said narratives, and a lot of it is driven by the production houses, but also driven by our clients who write these stories either on the spec script that they’d like to set up these production homes.”

The agents also discussed the importance of allyship and the ways Hollywood and businesses have moved forward in their endeavors to support LGBTQ+ representation.

Fenton said there’s still a way for Hollywood to go to further normalization. “I think it equally important to shift their representation on screen to not being the story, but being part of the story.”

Watch the full conversation below.

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Computer Science > Computer Vision and Pattern Recognition

Title: multi-scale representation learning for image restoration with state-space model.

Abstract: Image restoration endeavors to reconstruct a high-quality, detail-rich image from a degraded counterpart, which is a pivotal process in photography and various computer vision systems. In real-world scenarios, different types of degradation can cause the loss of image details at various scales and degrade image contrast. Existing methods predominantly rely on CNN and Transformer to capture multi-scale representations. However, these methods are often limited by the high computational complexity of Transformers and the constrained receptive field of CNN, which hinder them from achieving superior performance and efficiency in image restoration. To address these challenges, we propose a novel Multi-Scale State-Space Model-based (MS-Mamba) for efficient image restoration that enhances the capacity for multi-scale representation learning through our proposed global and regional SSM modules. Additionally, an Adaptive Gradient Block (AGB) and a Residual Fourier Block (RFB) are proposed to improve the network's detail extraction capabilities by capturing gradients in various directions and facilitating learning details in the frequency domain. Extensive experiments on nine public benchmarks across four classic image restoration tasks, image deraining, dehazing, denoising, and low-light enhancement, demonstrate that our proposed method achieves new state-of-the-art performance while maintaining low computational complexity. The source code will be publicly available.

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