Data Representation
Cambridge O Level Computer Science 2210 Topic 1 revision chapter covering number systems (why computers use binary, denary, binary and hexadecimal place value, conversion in both directions between denary, binary and hexadecimal up to 16 bits, why hexadecimal is used, addition of two positive 8-bit binary integers, overflow in a fixed-width register, logical left and right shifts including multiple shifts and discarded bits, and the two's complement representation of positive and negative 8-bit integers), text, sound and image representation (character sets including ASCII and Unicode, sampling an analogue sound wave with a stated sample rate and sample resolution, and bitmap images described by resolution and colour depth), and data storage and compression (the bit, nibble, byte and the 1024-based kibibyte to exbibyte ladder, calculating the file size of an image and a sound file from given information, the purpose of compression, and lossy and lossless methods including run-length encoding).Show moreShow less
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What is Data Representation about?
Every form of data a computer handles — a number, a character, a sound, an image — is converted into binary before it can be processed or stored. The conversion is done by an agreed encoding rule: place value for numbers, a character set for text, sampling for sound, pixels and colour depth for images. The binary is then held in fixed-width registers and processed using logic gates. Nothing about the pattern 01000001 tells you whether it means the number 65, the character A, one sample of a sound or one pixel of an image — only the rule you were told to apply does.
Topic 1 is assessed in Paper 1: Computer Systems. Paper 1 is a written paper of 1 hour 45 minutes carrying 75 marks, made up of short-answer and structured questions set on Topics 1 to 6. All questions are compulsory, candidates answer on the question paper, the paper is externally assessed, and calculators are not allowed. That last point shapes how you must revise: every conversion, every addition and every file-size calculation in this chapter has to be doable with a pen.
A computer represents all forms of data in binary, a number system with only two digits, 0 and 1. The reason is physical: the electronic circuits inside a computer can reliably hold and detect two stable states — for example a higher or a lower voltage — and those two states map directly onto the two binary digits. Data in that form is processed using logic gates and is stored, along with instructions, in registers. Any form of data therefore has to be converted into binary before the computer can process it.
In any number system, a digit's value depends on which column it is in. Reading right to left, each column is worth the base times the column before it. In binary the columns are the powers of two: 1, 2, 4, 8, 16, 32, 64, 128… In hexadecimal they are the powers of sixteen: 1, 16, 256, 4096… Reading a number in any base is then just "multiply each digit by its column value and add the results".
Three pairs of conversions are examinable, and each must be done in both directions, giving six routes in total. The conditions are fixed: integers only, positive values only in this outcome, a maximum length of 16 bits, and every calculation must be possible without a calculator.
Hexadecimal is used because it is easier for people to understand than binary: it is a much shorter representation of the same bit pattern, and each hexadecimal digit maps to exactly four bits, so converting between the two is quick and needs no arithmetic. A shorter string is quicker to read, quicker to write, quicker to say aloud and far less likely to be copied down wrongly. Hexadecimal is a notation for humans — the machine still stores the same binary.
Key ideas to remember
- One sentence for the whole chapter: data becomes binary by an agreed rule, lives in a register of fixed width, and only becomes meaningful again when the same rule is applied in reverse.
- Final self-test, no notes: convert 165 to binary and to hexadecimal; add your binary answer to 01110001 and say whether it overflows; then state what 10100101 means as an unsigned value and as a two's-complement value. If all four parts come out clean, Chapter 1 is secure.
What you need to be able to do
- Explain how and why a computer uses binary to represent every form of data.
- State that denary is base 10, binary is base 2 and hexadecimal is base 16, and use the place values of each.
- Convert, in both directions, between positive denary and positive binary; positive denary and positive hexadecimal; and positive hexadecimal and positive binary — integers only, up to 16 bits, with no calculator.
- Explain why hexadecimal is a useful way for people to represent binary, and identify areas of computer science in which it is used.
- Add two positive 8-bit binary integers, showing carries and the final 8-bit result.
- Explain what an overflow error is and why it occurs in binary addition in a register of fixed width.
- Perform logical left and right shifts, including multiple shifts, on a positive 8-bit binary integer, state which bits are lost, and state the effect on the value.
- Represent positive and negative 8-bit integers in two's complement, and convert in both directions between two's complement and denary or plain binary.
- Explain how and why a computer represents text, and describe the role of a character set, including ASCII and Unicode.
- Explain how and why a computer represents sound, define sample rate and sample resolution, and describe the effect of changing each on accuracy and file size.
- Explain how and why a computer represents an image, define resolution and colour depth, and describe the effect of changing each on quality and file size.
- State how data storage is measured, from bit and nibble through byte, KiB, MiB, GiB, TiB, PiB and EiB, and convert between them using 1024.
- Calculate the file size of an image file and of a sound file from the information given, and answer in the unit the question specifies.
- Explain the purpose of and need for data compression, including its effects on storage space, bandwidth and transmission time.
- Explain how files are compressed by lossy and lossless methods, including run-length encoding, and choose the appropriate method for a given scenario.
Key terms in Data Representation
- Place Value
- Place value is the worth attached to a digit because of the column it occupies, where each column is worth the base times the column to its right — powers of 2 in binary and powers of 16 in hexadecimal.
- Denary
- Denary is the base 10 number system used by people, with the ten digits 0 to 9 and column values that are powers of ten.
- Logical Shift
- A logical shift moves every bit in a register a stated number of places left or right; bits shifted out of the end of the register are lost and zeros are shifted in at the opposite end, multiplying or dividing a positive integer by two per place while no significant bits are lost.
- Binary
- Binary is the base 2 number system, using only the digits 0 and 1, in which a computer represents and processes all forms of data because its circuits have two stable states.
- Unicode
- Unicode is a character set that allows for a greater range of characters and symbols than ASCII, including different languages and emojis, and requires more bits per character than ASCII.
- Hexadecimal
- Hexadecimal is the base 16 number system, using the digits 0 to 9 and the letters A to F for the values 10 to 15, in which each hexadecimal digit represents exactly four binary bits.
- ASCII
- ASCII, the American Standard Code for Information Interchange, is a character set that represents each character with a small number of bits, covering the English letters, digits, punctuation and control characters.
- Image File Size
- Image file size is the storage an uncompressed bitmap requires, found by multiplying the image width in pixels by its height in pixels by the colour depth in bits, giving an answer in bits that is divided by 8 for bytes.
- Character Set
- A character set is an agreed table that gives every character a unique character code, so that text can be converted to binary for a computer to store and process.
- Base Conversion
- Base conversion is the process of rewriting the same numeric value in a different number system, covering the six conversions required at this level: denary to and from binary, denary to and from hexadecimal, and binary to and from hexadecimal.
- Two's Complement
- Two's complement is a method of representing positive and negative integers in binary in which the most significant column carries a negative place value, so an 8-bit pattern represents any integer from minus 128 to plus 127 with a single representation of zero.
- Lossy Compression
- Lossy compression reduces the file size by permanently removing data, so the original file cannot be reconstructed exactly and quality may be reduced.
- Image Resolution
- Image resolution is the number of pixels in an image; for a rectangular bitmap it is found by multiplying the width in pixels by the height in pixels.
- Sound File Size
- Sound file size is the storage an uncompressed recording requires, found by multiplying the sample rate by the sample resolution by the length of the recording in seconds, giving an answer in bits that is divided by 8 for bytes.
- Sample Resolution
- The sample resolution is the number of bits used per sample when an analogue sound wave is converted to binary. More bits per sample record the amplitude more precisely, giving better sound quality but a larger file.
- Sample Rate
- The sample rate is the number of samples taken in a second when an analogue sound wave is converted to binary. A higher sample rate follows the wave more closely, giving a more accurate recording but a larger sound file.
- Binary Addition
- Binary addition is the column-by-column addition of binary integers using the rules 0+0=0, 0+1=1 and 1+1=10 carry 1, where a carry out of the leftmost column of a fixed-width register is an overflow.
- Overflow
- An overflow error occurs when the result of a calculation is outside the range a fixed-width register can represent, for example a value above 255 in an 8-bit unsigned register, so the correct result cannot be stored or returned.
- Pixel
- A pixel is one of the small squares that make up a bitmap image; the colour of each pixel is stored as a binary value. The number of pixels sets the image resolution and the bits per pixel set the colour depth, so both increase the file size.
- Uses of Hexadecimal
- Hexadecimal is used wherever people must read, write or copy binary values, because one hexadecimal digit stands for exactly four bits and so shortens a binary string to a quarter of its length, making it quicker to read and less error-prone to transcribe.
- Data Compression
- Data compression is the process of reducing the size of a file, so that it requires less storage space, needs less bandwidth and takes less time to transmit.
- Colour Depth
- Colour depth is the number of bits used to represent the colour of each pixel; a colour depth of n bits gives two to the power n possible colours.
- Lossless Compression
- Lossless compression reduces the file size without permanently losing any data, so the original file can be reconstructed exactly; run-length encoding is an example.
- Run-Length Encoding
- Run-length encoding is a lossless compression method that replaces a run of consecutive identical values with the value and the number of times it repeats, so the original data can be rebuilt exactly.
- Data Storage Units
- Data storage units are the fixed-size quantities used to measure stored data, starting at the bit and rising through the nibble and byte to the kibibyte and beyond, where each unit above the byte is 1024 times the one below it.
Common mistakes to avoid
- 1. Treating a leading zero as optional. Why it fails A register has a fixed width. In an 8-bit register the value 12 is 00001100, not 1100. Inside a hexadecimal-to-binary conversion, 5 must become 0101, not 101, or every bit after it shifts one place and the whole answer is wrong. Fix Decide the width before you write anything, then pad on the left to fill it.
- 2. Calling every carry an overflow. Why it fails Carries happen inside almost every binary addition and are completely normal. An overflow error is different: the correct answer is too large for the register to hold. Fix Only the carry out of the leftmost column of an 8-bit unsigned addition signals overflow. See section 1.1 F.
- 3. Assuming a left shift always doubles. Why it fails It doubles only while no significant bit falls off the left-hand end. Shift 10110010 (178) left once and you get 01100100, which is 100 — not 356. Fix Look at the bits about to leave the register before claiming the multiplication still holds.
- 4. Reading the most significant bit as a minus sign. Why it fails In two's complement the leading 1 is not a sign symbol attached to the rest; it is a place value of −128. Reading 11010011 as "minus 1010011" gives −83. The correct value is −45. Fix Either use the signed place values with −128 at the left, or invert and add 1. See section 1.1 H.
- 5. Swapping sample rate and sample resolution. Why it fails They are different quantities with different units. Rate is samples per second; resolution is bits per sample. An "explain" answer that swaps them scores nothing even if the general idea is right. Fix Rate counts how often; resolution counts how precisely.
- 6. Stopping a file-size calculation at width × height. Why it fails That gives the number of pixels, not the size. Every pixel still has to be multiplied by the colour depth, and the result then converted to the unit requested. Fix Say the sentence "pixels, then bits, then bytes, then the unit asked for" at the start of every image question.
- 7. Dividing by 1000. Why it fails This topic uses the binary units. 1 KiB is 1024 bytes, 1 MiB is 1024 KiB. Using 1000 gives an answer that is wrong by roughly 2.4% per step and gains no marks. Fix Write "÷ 1024" in the margin before you begin, and give the answer in the unit named in the question.
- M1. "Binary is used only for numbers." Why it fails It confuses one use of binary with binary itself. Text, sound and images are all stored in binary too — only the encoding rule differs. Correct model Any form of data must be converted to binary to be processed by a computer, because its circuits have two stable states. Exam-safe "All forms of data, including text, sound and images, are converted to binary so that the computer can process them." Test yourselfHideQ. Name three non-numeric forms of data that are stored in binary.A. Text, sound and images.
- M2. "Hexadecimal is a form of compression." Why it fails Compression reduces the number of bits stored. Hexadecimal changes only how the same bits are written for a person to read. Correct model Hexadecimal is a notation. FF and 11111111 are the same eight bits in storage. Exam-safe "Hexadecimal is a shorter way for humans to write binary; it does not change the amount of data stored." Test yourselfHideQ. How many bits does the value FF occupy in memory?A. Eight — the same as 11111111.
- M3. "A shorter hexadecimal string means less underlying data." Why it fails The length of the written string is a property of the notation, not of the storage. One hexadecimal digit always stands for four bits. Correct model A 4-digit hexadecimal value is always 16 bits, however short it looks next to the binary. Exam-safe "Each hexadecimal digit represents four bits, so a shorter written form still describes exactly the same number of bits." Test yourselfHideQ. How many bits does the hexadecimal value A35F represent?A. 4 digits × 4 bits = 16 bits.
- M4. "Any carry means overflow." Why it fails Carries occur inside almost every binary addition and are ordinary arithmetic. Only a carry out of the leftmost column of the register signals a problem. Correct model Overflow means the correct result lies outside the register's range, not that a column overflowed into the next one. Exam-safe "A carry between columns is normal; an overflow error occurs only when the result is outside the range the register can represent." Test yourselfHideQ. 90 + 45 in an 8-bit register produces four carries. Is that an overflow?A. No — the total 135 is not greater than 255, so it fits.
- M5. "An 8-bit unsigned register can store 256." Why it fails It confuses the number of values with the largest value. Eight bits give 256 different patterns, but one of them is used for zero. Correct model 28 = 256 values, running from 0 to 255. The largest is 28 − 1. Exam-safe "An 8-bit unsigned register represents 256 different values, from 0 to 255, so the largest value it can hold is 255." Test yourselfHideQ. How many values, and what is the largest, for a 16-bit unsigned register?A. 65 536 values; largest 65 535.
- M6. "A logical shift wraps the discarded bits around." Why it fails That describes a rotation, which is a different operation. In a logical shift the bits leaving the register are lost. Correct model Bits shifted out are lost; zeros are shifted in at the opposite end. Exam-safe "Bits shifted out of the end of the register are lost and zeros are shifted in at the opposite end." Test yourselfHideQ. Shift 10000001 left one place. What is the result?A. 00000010. The leading 1 is lost, not moved to the right-hand end.
- M7. "A left shift always doubles the value." Why it fails It doubles only while no 1 falls off the left-hand end. Once a significant bit is lost, the result is not twice the original. Correct model Each place of left shift multiplies by two provided no significant bits are lost. Exam-safe "A logical left shift multiplies the value by two for each place shifted, as long as no significant bits are shifted out of the register." Test yourselfHideQ. 10110010 is 178. Shift left one place. Is the result 356?A. No — it is 01100100 = 100, because the bit worth 128 was discarded.
- M8. "The most significant bit is simply a minus sign." Why it fails In two's complement the leading 1 is a place value of −128 that is added to the rest — it is not a symbol you can detach and ignore. Correct model Read 11010011 as −128 + 64 + 16 + 2 + 1 = −45, not as "minus 1010011" = −83. Exam-safe "In two's complement the most significant bit has a place value of −128; a leading 1 indicates a negative number but the other bits still add positive values to it." Test yourselfHideQ. What denary value is the two's-complement pattern 11111111?A. −1, not −127.
- M9. "Two's complement has both a positive and a negative zero." Why it fails That is true of some other signed schemes, but not two's complement. Here 10000000 is already taken — it means −128. Correct model There is exactly one zero, 00000000. That is why the range −128 to +127 is lopsided. Exam-safe "Two's complement has a single representation of zero, which is why an 8-bit range runs from −128 to +127." Test yourselfHideQ. What does 10000000 represent in 8-bit two's complement?A. −128.
- M10. "ASCII stores the visual shape of a letter." Why it fails A character set stores a code number. The shape comes from a font, which is separate data. Correct model Character → character code → binary. The font is applied only when the character is drawn. Exam-safe "A character set maps each character to a code number which is stored in binary; the shape displayed is determined separately by the font." Test yourselfHideQ. A document's font is changed from one typeface to another. Do the stored character codes change?A. No. Only the shapes drawn on screen change.
- M11. "Unicode is a font." Why it fails A font is a set of shapes for drawing characters. Unicode is a character set: it assigns code numbers. Correct model Unicode allows for a greater range of characters and symbols than ASCII, including different languages and emojis, and requires more bits per character. Exam-safe "Unicode is a character set, not a font; it assigns a code to a far greater range of characters than ASCII." Test yourselfHideQ. Give one advantage and one disadvantage of Unicode over ASCII.A. Advantage: a greater range of characters and symbols, including different languages and emojis. Disadvantage: it requires more bits per character, so files are larger.
- M12. "Sample rate and sample resolution mean the same thing." Why it fails They are different quantities measured in different things. Rate counts samples per second; resolution counts bits per sample. Correct model Rate is how often the wave is measured; resolution is how precisely each measurement is recorded. Exam-safe "The sample rate is the number of samples taken in a second; the sample resolution is the number of bits used per sample." Test yourselfHideQ. Which one determines how many different amplitude levels are available?A. The sample resolution: n bits give 2n levels.
- M13. "Increasing the sample rate increases the pitch." Why it fails It confuses the frequency of the recorded sound with the frequency of the sampling. Pitch is a property of the sound; the sample rate is a setting of the recording process. Correct model A higher sample rate takes more measurements of the same wave, giving a more accurate representation and a larger file. The pitch is unchanged. Exam-safe "Increasing the sample rate takes more samples per second, which makes the stored recording more accurate and increases the file size; it does not change the pitch of the sound." Test yourselfHideQ. State two effects of doubling the sample rate.A. The stored recording is a more accurate representation of the original wave, and the file size doubles.
- M14. "Sample resolution is the volume." Why it fails Resolution is the number of bits available to describe each amplitude measurement, not the size of the amplitude itself. Correct model More bits per sample means each amplitude is recorded more precisely, not that the sound plays back louder. Exam-safe "The sample resolution is the number of bits per sample; it affects how accurately each amplitude is recorded, not how loud the playback is." Test yourselfHideQ. How many amplitude levels does a 4-bit sample resolution give?A. 24 = 16.
- M15. "Colour depth means the number of pixels." Why it fails It swaps the two image settings. The number of pixels is the resolution. Correct model Colour depth is the number of bits used to represent the colour of each pixel. Exam-safe "The colour depth is the number of bits used to represent each colour; the resolution is the number of pixels in the image." Test yourselfHideQ. An image is 200 × 100 pixels with 8-bit colour depth. Which number is the resolution?A. 20 000 pixels. The 8 is the colour depth.
- M16. "Resolution means the number of colours." Why it fails The same swap in the other direction. The number of colours comes from the colour depth, as 2depth. Correct model Resolution counts pixels. Colours = 2colour depth. Exam-safe "The resolution is the number of pixels in the image; the number of possible colours is two to the power of the colour depth." Test yourselfHideQ. How many colours are available at a colour depth of 24 bits?A. 224 = 16 777 216.
- M17. "File size is width × height." Why it fails That gives the number of pixels. It says nothing about how many bits each pixel occupies. Correct model File size in bits = width × height × colour depth, then convert to the unit requested. Exam-safe "File size in bits equals the number of pixels multiplied by the colour depth." Test yourselfHideQ. A 100 × 100 image has 8-bit colour depth. What is 10 000 — the pixels or the size in bits?A. The pixels. The size is 10 000 × 8 = 80 000 bits.
- M18. "One byte contains four bits." Why it fails Four bits is a nibble. Halving the byte halves every subsequent conversion. Correct model 4 bits = 1 nibble; 8 bits = 1 byte; 2 nibbles = 1 byte. Exam-safe "There are 8 bits in a byte and 4 bits in a nibble." Test yourselfHideQ. How many bits in 2 KiB?A. 2 × 1024 × 8 = 16 384 bits.
- M19. "One KiB contains 1000 bytes." Why it fails The units in this topic are the binary ones. Using 1000 introduces an error of about 2.4% at every step, compounding as you climb. Correct model 1 KiB = 1024 bytes, and every step above the byte is ×1024. Exam-safe "Calculations must use 1024, so 1 KiB is 1024 bytes and 1 MiB is 1024 KiB." Test yourselfHideQ. How many bytes in 1 MiB?A. 1024 × 1024 = 1 048 576.
- M20. "Lossy compression can always recreate the original." Why it fails Lossy removes data permanently. Decompression can only redistribute what survived. Correct model Lossy gives back an approximation; only lossless gives back the exact original. Exam-safe "Lossy compression permanently removes data, so the original file cannot be reconstructed exactly." Test yourselfHideQ. Which method must be used for a program file, and why?A. Lossless, because the file must be reconstructed exactly or it will not run correctly.
- M21. "Lossless compression always produces a smaller file, and RLE works equally well on all data." Why it fails Lossless methods exploit patterns. Where there is no pattern there is nothing to exploit, and RLE in particular stores two items for every run — so data with no repetition gets bigger. Correct model RLE is most effective on data containing long runs of identical values, such as a two-colour logo with large flat areas. On a detailed photograph the runs are one pixel long and the encoded form can exceed the original. Exam-safe "Run-length encoding reduces file size only when the data contains long runs of repeated values; with little repetition each single value is stored as a pair, so the file may not shrink and could grow." Test yourselfHideQ. Apply RLE to ABCDEF and count the items.A. 1A 1B 1C 1D 1E 1F — 6 pairs = 12 items, against 6 originally. It has doubled.
Examiner tips
- How to use this chapter. Read a teaching section, work its example on paper before opening the answer, then use the matching tool in the interactive tools section only to check your own working. The tools cannot be taken into the exam; the written methods can.
- Marks live in the working. In a Topic 1 calculation the final number is often worth one mark out of three. A wrong final answer with correct, clearly labelled working still earns most of the marks; a right answer with no working can earn one.
- The shortcut worth knowing. There is no direct route between denary and hexadecimal that is faster than going through binary for small values, but for anything over one byte the repeated-division method is quicker. And hexadecimal and binary convert directly, four bits at a time, with no arithmetic at all — so if you are ever asked for denary to hexadecimal and get stuck, convert to binary first, then group in fours.
- The seven things to state in a shift answer the original bit pattern; the direction of the shift; the number of places; which bits were discarded; the final 8-bit pattern (all eight bits, zeros included); the denary result; whether the simple ×2 or ÷2 interpretation still holds. Points 4 and 7 are where most marks are lost. Never answer a shift question without checking what fell off the end.
- State your assumptions. These calculations assume the data is uncompressed, that there is no metadata or file header unless the question supplies one, and that the colour depth applies to every pixel. If a question does give a header size, add it after converting to a common unit — never before.
- State your convention. RLE can be written run-length-first (4A 3B) or value-first (A4 B3). Both are valid; what is not valid is leaving the reader to guess. Write one line before your answer: "Format used: run length followed by value." This chapter uses run length then value throughout.
- How to use them well. Cover the tool. Do the question. Reveal the tool. If your answer differs, do not simply copy the tool's number — find the line where the two of you diverge. That line is the habit worth fixing.
- Two rules that make the schedule work. First, always attempt before you look — producing a wrong answer and correcting it builds far more durable memory than reading a right one. Second, if a session takes noticeably longer than the time shown, that is data, not failure: it tells you which competency to put in the next session.
Frequently asked questions
What is the difference between binary, denary and hexadecimal?
Denary is base 10, the number system people normally use, with column values that are powers of ten. Binary is base 2, using only the digits 0 and 1 with column values that are powers of two — the only form a computer actually stores. Hexadecimal is base 16, using the digits 0 to 9 and the letters A to F, with column values that are powers of sixteen. Each hexadecimal digit represents exactly four binary bits, so it is a much shorter way for people to write the same bit pattern.
Why do computers use binary to represent all forms of data?
A computer represents all data in binary because its electronic circuits can reliably hold and detect only two stable states, such as a higher or a lower voltage, which map directly onto the two binary digits 0 and 1. Data in that form is processed using logic gates and stored, along with instructions, in registers. So any form of data — a number, text, sound or an image — has to be converted into binary before the computer can process it.
What is an overflow error, and when does it occur in an 8-bit register?
An overflow error occurs when a calculation produces a value outside the range a fixed-width register can represent, so the correct result cannot be stored or returned. An 8-bit unsigned register can hold values from 0 to 255; if an addition produces a result greater than 255, the correct answer needs a ninth bit, and there is no ninth bit to put it in, so overflow occurs. A carry between columns during addition is normal and is not, by itself, overflow.
Does a logical left shift always double the value of a binary number?
No. A logical left shift multiplies a positive value by two for each place shifted only while no significant bit is lost off the left-hand end of the register. Shifting 10110010 (178) left by one place gives 01100100, which is 100, not 356, because the bit worth 128 was shifted out and lost. Bits shifted off the end are gone; zeros are shifted in behind them, so the doubling rule breaks down once a 1 falls off.
What is the difference between sample rate and sample resolution?
Sample rate is the number of samples taken of an analogue sound wave in one second; sample resolution is the number of bits used to store each of those samples. Increasing the sample rate takes more measurements per second, so the recording follows the wave more closely; increasing the sample resolution records each amplitude more precisely. Both changes make the stored recording more accurate but increase the file size — the two settings must never be swapped in an answer.
Why must file-size and storage calculations use 1024 rather than 1000?
This topic uses the binary storage units: 1 kibibyte (KiB) is 1024 bytes, 1 mebibyte (MiB) is 1024 KiB, and every unit above the byte is 1024 times the one below it. Using 1000 instead introduces an error of roughly 2.4% at every step, which compounds as the calculation climbs through the units, so an answer that divides by 1000 will not match the expected value and gains no marks. Always divide by 1024 and give the answer in the unit the question names.
How do you read a negative number stored in two's complement?
In an 8-bit two's complement number the leftmost (most significant) bit has a place value of −128 instead of +128; every other column keeps its usual positive value. Read the pattern by adding the place values of every 1 bit, including the negative one. For example, 11010011 is −128 + 64 + 16 + 2 + 1 = −45 — not "minus 1010011", which would wrongly give −83. This lets one 8-bit pattern represent any integer from −128 to +127, with a single representation of zero.
Syllabus reference and sources
Written against: Cambridge O Level Computer Science (2210) 2026–2028 Syllabus (Subject Content, Topic 1: Data Representation).
Written by: Academiq Edu Instructor Panel
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