Data Representation and Number Systems
Data Representation and Number Systems tests fluency with binary, hexadecimal and character coding, plus how analogue images and sound become digital. Questions often require a conversion, a file-size calculation or an explanation of why a particular representation is used.
Number bases and units
- Binary is base 2 with place values 1, 2, 4, 8 and so on; denary is base 10; hexadecimal is base 16, using 0-9 and A-F.
- Group binary digits in fours to convert to hex: 1011 1110 = BE.
- 1 byte = 8 bits; 1 KiB = 1024 bytes; 1 MiB = 1024 KiB. Transfer rates are usually bits per second, so divide by 8 for bytes per second.
Representing integers and characters
- Unsigned binary represents only non-negative values. Two's complement represents negatives: invert the bits and add 1. In 8 bits the range is -128 to +127.
- ASCII uses 7-bit codes for English characters; Unicode uses larger code spaces to cover many scripts and symbols.
Images and sound
- Bitmap images store a grid of pixels; colour depth is bits per pixel and resolution is pixel dimensions. File size is approximately width × height × colour depth ÷ 8.
- Sound is sampled at a sample rate, in samples per second, and quantised to a bit depth. Higher rates and depths improve fidelity but increase file size.
Worked example
Convert 11011010 to denary and hex. Place values give 128 + 64 + 16 + 8 + 2 = 218. Split into nibbles: 1101 = D and 1010 = A, so the hex value is DA.
Traps
Mixing up place values; forgetting that hex A-F are single digits; treating the leftmost bit as a sign in unsigned work; and confusing sample rate with bit depth. In file-size questions, keep bits and bytes consistent throughout.