Data representation

ZIMSEC O Level · Computer Science · Form 2, Form 3

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Computers store all data as binary digits (bits): 0 or 1.

Units

8 bits = 1 byte; 1 kilobyte (KB) = 1 024 bytes; 1 MB = 1 024 KB; 1 GB = 1 024 MB; 1 TB = 1 024 GB.

Binary numbers

Place values in an 8-bit byte: 128, 64, 32, 16, 8, 4, 2, 1.

Worked example: Convert 01011010 to denary.

64 + 16 + 8 + 2 = 90

Worked example: Convert 45 to 8-bit binary.

45 = 32 + 8 + 4 + 1 → 00101101

Hexadecimal

Base 16: digits 0–9 and A–F (A = 10 … F = 15). Each hex digit stands for 4 bits, so hex is a short way to write binary (used for colour codes and memory addresses).

Worked example: Convert 1011 1110 to hexadecimal.

1011 = 11 = B and 1110 = 14 = E → BE

Text, images and sound

Text: each character has a code (ASCII uses 7 or 8 bits; Unicode covers all world languages).
Images: made of pixels; more pixels (resolution) and more colours (colour depth) mean larger files.
Sound: sampled many times per second; higher sample rate means better quality and larger files.

Compression

Lossless (no data lost, e.g. ZIP) and lossy (some detail removed, e.g. JPEG, MP3) reduce file size.

Exam tip: Write the place values above the bits before converting – it prevents mistakes.

Check yourself

Convert 11001000 to denary.
Convert 3F (hex) to denary.
How many bytes are in 2 KB?

Show answers

128 + 64 + 8 = 200
3 × 16 + 15 = 63
2 048 bytes

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