Computer Fundamentals and Number Systems
The Computer Fundamentals and Number Systems domain checks whether you can describe how a computer is organised and whether you can move confidently between decimal, binary, octal and hexadecimal representations. Board papers usually pair a definitions question (stored-program model, primary versus secondary memory, hardware versus software) with a conversion or a 1's/2's complement calculation.
Core rules
- A computer follows the stored-program model: input → CPU (ALU plus control unit) → memory → output, with instructions fetched, decoded and executed one at a time.
- Memory units scale by 1024: 8 bits = 1 byte, 1024 B = 1 KB, 1024 KB = 1 MB, 1024 MB = 1 GB.
- Every positional system uses weights of its base. Binary weights are 1, 2, 4, 8, 16, 32, ...; hex digits A–F stand for 10–15.
- Decimal to any base: divide repeatedly by the base and read the remainders bottom-up. Any base to decimal: multiply each digit by its weight and add.
- Binary to octal or hex is a grouping shortcut: 3 bits per octal digit, 4 bits per hex digit, grouping from the right.
- 2's complement = 1's complement + 1; it stores negatives so that subtraction becomes addition.
Worked example
Convert 156 to binary and hexadecimal.
- Largest power of 2 not exceeding 156 is 128, and 156 − 128 = 28.
- 16 fits (28 − 16 = 12), 8 fits (12 − 8 = 4), 4 fits (4 − 4 = 0).
- Set bits at 128, 16, 8, 4: 10011100.
- Group from the right in fours: 1001 1100 → 9C. So 156 in decimal = 10011100 in binary = 9C in hexadecimal.
Traps
- Reading division remainders top-down instead of bottom-up.
- Forgetting that in a signed byte the leftmost bit is a sign bit, so 10011100 is −100, not 156.
- Padding hex groups from the left rather than the right.
- Writing 1 KB = 1000 bytes in a board answer.