Computer Fundamentals and Number Systems
BSEH Secondary Computer Science tests computer fundamentals through number-system conversions, data representation and basic computer organisation.
Positional number systems
A number system is defined by its base (radix) and the place values it assigns. Binary (base 2) uses 0–1, octal (base 8) uses 0–7, decimal (base 10) uses 0–9, and hexadecimal (base 16) uses 0–9 plus A–F for 10–15. In any base, the rightmost digit has weight b^0, the next b^1, and so on. To convert decimal to another base, divide repeatedly by the target base and read remainders bottom-up. To convert binary to octal or hexadecimal, group bits in threes or fours from the right and pad the leftmost group with zeros.
Complements and codes
Computers store signed integers using two’s complement: invert all bits (one’s complement) and add 1. The leftmost bit indicates sign in a fixed-width representation. Character codes map symbols to numbers; ASCII covers English letters and control characters, while Unicode covers multilingual scripts.
Worked example
Convert decimal 45 to binary and hexadecimal. Subtracting place values: 45 = 32 + 8 + 4 + 1, so the 8-bit binary form is 00101101. Group from the right into nibbles: 0010 1101, which is 2D in hexadecimal. Check: 2 × 16 + 13 = 45.
Traps that cost marks
- Writing 101101 without showing the 8-bit padding when a fixed width is requested.
- Reading remainders top-down instead of bottom-up.
- Confusing subscript notation such as 1011₂ with a decimal value.
- Forgetting that two’s complement changes both the bit pattern and the interpreted value.