Data Representation and Number Systems
What the exam tests
This domain tests how computers represent numbers, text, images and sound using binary. You must convert between binary, denary and hexadecimal, use two’s complement for signed integers, and explain character-coding standards.
Core rules
- Binary is base 2; each position has weight 2^n. Hexadecimal is base 16 and groups four binary bits per hex digit.
- A nibble is 4 bits; a byte is 8 bits. 1 KiB = 1024 bytes, while storage manufacturers often use 1 KB = 1000 bytes.
- Two’s complement represents signed integers. For an 8-bit number, invert all bits of the positive value and add 1. Range is −128 to +127.
- ASCII uses 7 or 8 bits; Unicode uses code points and supports multilingual text.
Worked example
Convert decimal 45 to binary and hex. 45 = 32 + 8 + 4 + 1, so the 8-bit pattern is 00101101. Group into nibbles: 0010 1101 = 2D in hexadecimal. Now represent −5 in 8-bit two’s complement: +5 = 00000101; invert = 11111010; add 1 = 11111011. Reasoning: the leftmost bit is 1, confirming a negative number; its magnitude is found by reversing the process.
Traps that cost marks
Do not drop leading zeros when an 8-bit answer is required. Do not mix positional weights. Do not write 1 KB = 1024 bytes without stating KiB. Do not confuse bits (b) with bytes (B). In two’s complement, do not use sign-and-magnitude inversion without adding 1. Check overflow when adding two signed numbers.
Exam focus
Expect direct conversions, signed-number ranges and short explanations of why Unicode is needed.