What number work does Topic 2 require?

You must determine the number of states a binary pattern can hold ($2^n$), convert between denary and 8-bit binary (unsigned 0 to 255 and two's complement -128 to +127), add two binary patterns and apply logical and arithmetic shifts, recognise overflow, convert between hexadecimal and binary, and calculate file sizes for images and sound and storage capacity using binary multiples. This number work appears in Paper 1 and rewards accuracy.

What is two's complement?

Two's complement is the standard way to store signed integers. The most significant bit is given a negative place value (in 8 bits it is -128), so a leading 1 means the number is negative and the range is -128 to +127. To write a negative number, convert the positive value to binary, invert every bit, then add 1. Ordinary binary addition then works for negative numbers, which is why processors use it.

Why is hexadecimal used?

Hexadecimal is a compact, readable shorthand for binary. One hex digit represents exactly four bits, so two hex digits make a byte, turning long binary strings into far fewer characters that people can read and write with fewer errors. The computer still stores binary; hex is a notation for humans, used for colour codes, memory addresses and machine code.

How do you calculate an image or sound file size?

For a bitmap image, the size in bits is width times height times colour depth; divide by 8 for bytes. For a sound file, the size in bits is sample rate times bit depth times duration in seconds; divide by 8 for bytes. Edexcel uses binary multiples for storage, so each step (byte to kibibyte to mebibyte) multiplies by 1024. Increasing resolution, colour depth, sample rate or bit depth improves quality but increases file size.

How should I revise Topic 2 for Paper 1?

Drill the conversions (denary, binary, hexadecimal and two's complement) and the binary addition and shift rules until they are automatic, because accuracy earns the marks. Learn the binary storage multiples (each 1024 of the one below) and practise file-size and capacity calculations. Learn the precise definitions of colour depth, resolution, sample rate, bit depth and lossy versus lossless compression.

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Edexcel GCSE Computer Science Topic 2 Data: binary, two's complement, hexadecimal, ASCII, images, sound, storage and compression

A deep-dive Edexcel GCSE Computer Science guide to Topic 2 Data. Covers why computers use binary and the number of states a pattern holds, unsigned and two's complement signed integers, denary-binary conversion, binary addition and shifts, overflow, hexadecimal, 7-bit ASCII, bitmap images, sampled sound, the binary storage multiples and file-size calculations, and lossy and lossless compression.

Generated by Claude Opus 4.815 min readTopic 2Updated 2026-06-02

Reviewed by: AI editorial process; not yet individually human-reviewed

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What Topic 2 actually demands
Binary, states and signed numbers
Binary arithmetic, shifts and hexadecimal
Encoding characters, images and sound
Storage and compression
Check your knowledge

What Topic 2 actually demands

Data is the most numerical part of the course and a major part of Paper 1. You must move fluently between the number representations, handle signed numbers in two's complement, add binary and shift bits, recall the binary storage units, and calculate file sizes and capacity. You also need to explain how characters, images and sound are encoded as binary, the limitations that a fixed number of bits imposes, and why and how data is compressed.

This guide ties together the seven dot-point pages for Topic 2.

Binary, states and signed numbers

Computers use binary because their components have two stable states that map to 1 and 0. A pattern of $n$ bits holds $2^n$ states. Whole numbers are stored as unsigned integers (8 bits give 0 to 255) or as two's complement signed integers (8 bits give -128 to +127, with the leftmost bit worth -128). Two's complement of a negative number is found by inverting the bits of the positive value and adding 1.

Binary arithmetic, shifts and hexadecimal

Binary addition adds column by column with carries, and overflow occurs when the result needs more bits than the register holds, so a bit is lost and the answer is wrong. A binary shift moves bits left (multiply by $2^n$ ) or right (divide by $2^n$ ); a logical shift fills with 0, while an arithmetic right shift copies the sign bit. Hexadecimal is a shorthand where one hex digit equals four bits, so converting to and from binary is done in nibbles.

Encoding characters, images and sound

7-bit ASCII maps each character to one of $2^7 = 128$ codes, with letters and digits in consecutive order. A bitmap image is a grid of pixels, where resolution (number of pixels) and colour depth (bits per pixel) set the quality and size. Sound is analogue, so it is sampled: the sample rate (samples per second) and bit depth (bits per sample) set the quality and size. A fixed number of bits limits the colours, amplitudes and detail that can be stored.

Storage and compression

Storage uses binary multiples: bit, nibble, byte, then kibibyte, mebibyte, gibibyte and tebibyte, each $1024$ of the one below. File-size and capacity calculations use these factors. Compression reduces file size to save storage and transfer faster: lossless keeps all the data so the original can be rebuilt exactly, while lossy permanently removes data for much smaller files (MP3, JPEG).

Check your knowledge

A mix of conversion, calculation and recall questions covering Topic 2. Attempt them, then check against the solutions.

State the number of states a 5-bit pattern can hold. (1 mark)
Convert the denary number 100 to 8-bit unsigned binary. (2 marks)
State the 8-bit two's complement range. (1 mark)
Convert the binary number 11001010 to hexadecimal. (2 marks)
State how many characters 7-bit ASCII can represent. (1 mark)
Calculate the file size in bytes of a 100 by 80 pixel image at 8 bits per pixel. (2 marks)
State how many bytes are in a kibibyte. (1 mark)
State one difference between lossy and lossless compression. (2 marks)

Solutions

Step 1: Q1 - number of states in a bit pattern

A pattern of $n$ bits can represent $2^n$ different states, because each bit doubles the number of combinations:

2^5 = 32 \text{ states}

Step 2: Q2 - denary to 8-bit binary

Write out the binary column headings (128, 64, 32, 16, 8, 4, 2, 1) and find which columns sum to 100: $64 + 32 + 4 = 100$ . Place a 1 in those columns and 0 elsewhere:

01100100

Step 3: Q3 - two's complement range

In 8-bit two's complement the most significant bit has place value $-128$ , giving a range from $-128$ (when only the top bit is 1) to $+127$ (when all other bits are 1).

Answer: $-128$ to $+127$ .

Step 4: Q4 - binary to hexadecimal

Group the 8 bits into two nibbles of 4 bits each, then convert each nibble separately using the hex table:

$1100 = 12 = \text{C}$ and $1010 = 10 = \text{A}$ , so the result is $\text{CA}$ .

Step 5: Q5 - 7-bit ASCII character count

The number of distinct characters is the number of 7-bit patterns, which is $2^7$ :

2^7 = 128 \text{ characters}

Step 6: Q6 - bitmap image file size

Multiply the number of pixels (width by height) by the colour depth in bits per pixel to get the size in bits, then divide by 8 to convert to bytes:

100 \times 80 \times 8 = 64000 \text{ bits}, \quad 64000 \div 8 = 8000 \text{ bytes}

Step 7: Q7 - kibibyte size

The binary storage multiples each multiply by 1024. A kibibyte is $2^{10} = 1024$ bytes.

Answer: 1024 bytes.

Step 8: Q8 - lossy versus lossless compression

The key distinction is whether the original file can be reconstructed perfectly. Lossy compression permanently discards some data to achieve smaller file sizes, so the original cannot be restored exactly. Lossless compression keeps all the data and the original can be rebuilt without any loss.

Sources & how we know this

Pearson Edexcel GCSE (9-1) Computer Science (1CP2) specification — Pearson (2020)