Computer Fundamentals and Number Systems
What this domain covers
The exam checks whether you can describe how a computer is organised and convert numbers between the bases used in hardware and programming. Expect block-diagram questions (input, CPU, output, with memory), generations of computers, and memory units such as bit, byte, KB, MB, GB and TB.
Core rules
- CPU = ALU (arithmetic and logic) + control unit + registers; it fetches, decodes and executes instructions.
- Primary memory (RAM, ROM) is accessed directly by the CPU; secondary storage (HDD, SSD, DVD) is not.
- In any base b, place values are powers of b counted from the right, starting at b^0 = 1.
- Binary to hex or octal works by grouping bits: 4 bits per hex digit, 3 bits per octal digit.
- 2's complement = invert all bits, then add 1; the leftmost bit carries the sign.
Worked example
Convert decimal 156 to binary and hex. Repeated division by 2: 156/2 = 78 r0; 78/2 = 39 r0; 39/2 = 19 r1; 19/2 = 9 r1; 9/2 = 4 r1; 4/2 = 2 r0; 2/2 = 1 r0; 1/2 = 0 r1. Reading remainders upward gives 10011100. Group into nibbles: 1001 1100, which is 9 and C, so 9C. Check: 128 + 16 + 8 + 4 = 156.
Traps
- Starting place values at 2 instead of 1.
- Writing the 1's complement when 2's complement is asked (omitting the +1).
- Reading remainders top-to-bottom instead of bottom-to-top.
- Saying 1 KB = 1000 bytes unless the question specifies decimal (SI) units.