Data Representation: Revision Notes

Condensed for the final weeks. For worked examples, use the Data Representation study guide, which covers Topic 1 (1.1 Number systems, 1.2 Text/sound/images, 1.3 Data storage and compression) in full for Cambridge IGCSE Computer Science 0478, 2026–2028 series. For further exam-style practice with worked answers on this topic, see the Data Representation practice questions.

Number conversions

Denary -> Binary : subtract place values 128 64 32 16 8 4 2 1
Binary -> Hex    : split into NIBBLES (4 bits), convert each
Hex digits       : 0-9 then A=10 B=11 C=12 D=13 E=14 F=15

Example  217  ->  11011001  ->  1101 1001  ->  D9

Hex is used because it is compact and readable for humans: MAC addresses, IPv6, colour codes, memory dumps, error codes.

Binary arithmetic

• Add column by column, carrying when the total reaches 2.
• Overflow — the result needs more bits than the register holds; the extra bit is lost and the answer is wrong.
• Logical shift left = ×2 per place. Right = ÷2 per place. Bits shifted out are lost.

Character sets

Set	Bits	Characters
ASCII	7	128
Extended ASCII	8	256
Unicode	16+	Very wide range of writing systems

Unicode supports a very wide range of languages and scripts but can produce larger file sizes than ASCII, though UTF-8 keeps ASCII characters at a single byte.

File size formulas

IMAGE  size (bits) = width x height x colour depth
SOUND  size (bits) = sample rate x sample resolution x seconds

bits -> bytes : / 8
bytes -> KiB  : / 1024      KiB -> MiB : / 1024

• Resolution = number of pixels. Colour depth = bits per pixel; n bits gives 2ⁿ colours.
• Sample rate = samples per second (Hz). Sample resolution = bits per sample.
• Increasing any of these improves quality and increases file size.

Two’s complement

Represents negative numbers in binary. The most significant bit has a negative place value:

8-bit place values:  -128  64  32  16  8  4  2  1

Example: represent -19
  19 in binary        = 00010011
  Flip every bit      = 11101100
  Add 1               = 11101101   <- this is -19

Check: -128+64+32+8+4+1 = -19 (correct)

To convert back to denary, sum the place values directly using the negative value for the leftmost bit — there is no need to reverse the flip-and-add-one process to read a two’s complement number.

Compression

	Lossless	Lossy
Data	All recoverable	Permanently discarded
Method	Removes redundancy (e.g. RLE)	Removes detail humans barely notice
File size	Larger	Much smaller
Use for	Text, program files, spreadsheets	Photos, music, video

Never use lossy for a file where every byte matters — a program would not run.

Run length encoding (RLE) replaces a run of identical repeated values with a single value-and-count pair:

Original:   WWWWWWWWWWWWBWWWWWWWWWWWWBBBWWWWWWWWWWWWWWWWWWWWWWWWBWWWWWWWWWWWWWW
RLE:        12W 1B 12W 3B 24W 1B 14W

RLE works best on images with large blocks of a single colour (simple graphics, icons); it barely helps a photograph, where colour varies pixel to pixel.

Data storage units

A nibble is 4 bits, and a byte is 8 bits (two nibbles). From the kibibyte upwards, each unit is 1024 times the one before it:

bit -> nibble (4 bits) -> byte (8 bits) -> kibibyte (KiB)
    -> mebibyte (MiB) -> gibibyte (GiB) -> tebibyte (TiB)
    -> pebibyte (PiB) -> exbibyte (EiB)

The “-bi-” (kibi, mebi, gibi…) naming makes explicit that the factor is 1024, not 1000 — a distinction the syllabus is specific about: it names only these binary units, and file-size calculations must use 1024.

Exam traps

• Divide by 1024, not 1000, for KiB and MiB.
• Don’t forget bits → bytes (÷8) before converting further.
• Sample rate vs sample resolution — these are different things.
• Hexadecimal is for human readability; the computer stores binary.
• Lossy compression is permanent — the data cannot be restored.
• In two’s complement, forgetting to add 1 after flipping the bits — the flip alone gives one’s complement, not two’s complement.
• Applying RLE to a photograph and expecting a large saving — natural images rarely have long runs of identical values, so lossy compression (e.g. JPEG) suits them far better.
• Labelling a 1024-based answer “KB” or “MB” — the syllabus units are KiB and MiB, and the answer must be in the unit the question asks for.

Self-test

1. Convert denary 174 to binary and hex.
2. An image is 1024 × 768 with 24-bit colour. Give the size in MiB.
3. What causes overflow?
4. Why is Unicode preferred over ASCII for a multilingual website?
5. Which compression type suits a spreadsheet, and why?
6. Represent −19 in 8-bit two’s complement.
7. Why does RLE compress a simple icon well but a photograph poorly?

Answers: 1. 10101110 → nibbles 1010 1110 → AE. 2. 1024×768×24 = 18,874,368 bits ÷ 8 = 2,359,296 bytes ÷ 1024 = 2304 KiB ÷ 1024 = 2.25 MiB. 3. The result of a calculation requires more bits than the register can hold, so the most significant bit is lost. 4. ASCII cannot represent non-Latin scripts; Unicode covers a very wide range of the world’s writing systems. 5. Lossless — any discarded data would corrupt values and formulas. 6. Write 19 as 00010011, flip every bit to get 11101100, then add 1 to get 11101101. 7. An icon typically has long runs of identical pixel values that RLE can replace with a single value-and-count pair, while a photograph’s colours vary almost pixel to pixel, giving very few long runs to compress.