Data Representation and Number Systems
Domain focus
Data Representation and Number Systems tests binary, decimal, octal and hexadecimal conversion, binary arithmetic, character coding, and how text, images and sound are stored as bits. O/L questions often require showing place values, not just the final answer.
Core rules and concepts
- 1 bit is a binary digit; 1 nibble = 4 bits; 1 byte = 8 bits; 1 KiB = 1024 bytes, while storage marketing may use 1 KB = 1000 bytes.
- Place values double leftwards: 128, 64, 32, 16, 8, 4, 2, 1 for one byte.
- Hexadecimal uses 0–9 and A–F; each hex digit represents 4 bits, so it is a compact way to write binary.
- Unsigned binary represents only non-negative values; two’s complement represents signed integers. An 8-bit two’s complement range is −128 to +127.
- ASCII covers English characters; Unicode supports many scripts and symbols.
- Images are stored as pixels with colour codes; sound is sampled at intervals and quantised into binary values.
Worked example
Convert decimal 45 to binary. Use place values: 45 − 32 = 13; 13 − 8 = 5; 5 − 4 = 1; 1 − 1 = 0. The bits for 32, 8, 4 and 1 are 1; the rest are 0, giving 101101. Pad to 8 bits: 00101101. Group into nibbles: 0010 1101 = 2D in hexadecimal. Reasoning: each 1 marks a place value included in the total; grouping by four bits converts binary to hex directly.
Traps that cost marks
Writing place values right-to-left incorrectly; forgetting leading zeros when a byte is required; using decimal arithmetic inside binary addition without carrying; confusing KiB with KB; treating ASCII and Unicode as identical; and misstating the signed range of an 8-bit two’s complement number.