Computer Fundamentals and Number Systems
What the examiner tests
This domain covers how a computer is organised and how numbers are written in different bases. Expect one-mark definitions, a block-diagram description, and a conversion such as binary to decimal or decimal to binary.
Core ideas
- A computer follows the input → process → output → storage cycle. The CPU (Central Processing Unit) is the processing unit; it contains the ALU for arithmetic and logic, and the CU for fetching, decoding and executing instructions.
- Memory is primary (RAM, ROM - directly accessible by the CPU) or secondary (hard disk, SSD, pen drive - permanent but slower).
- A number system is defined by its base (radix), which equals the number of distinct digits. Binary base 2 uses 0–1; octal base 8 uses 0–7; decimal base 10 uses 0–9; hexadecimal base 16 uses 0–9 and A–F, where A = 10 and F = 15.
- Positional value: each digit is multiplied by base^position, counting positions from 0 at the radix point, moving left for the integer part and right for the fraction.
- A bit is one binary digit; 8 bits = 1 byte; 4 bits = 1 nibble.
Worked example
Convert 1101.01₂ to decimal. Write weights from the left: 8, 4, 2, 1 for the integer part, and 0.5, 0.25 for the fraction. = 1×8 + 1×4 + 0×2 + 1×1 + 0×0.5 + 1×0.25 = 8 + 4 + 0 + 1 + 0 + 0.25 = 13.25₁₀.
Traps
- Counting the first position as 1 instead of 0.
- Treating 10₂, 10₈ and 10₁₀ as the same value - they are 2, 8 and 10.
- Confusing bit and byte, or writing “KB” when the examiner wants the binary definition of 1024 bytes.
- Forgetting that hexadecimal digits beyond 9 are letters.