Introduction
A number system is simply a way of writing numbers using a fixed set of symbols (digits) and a rule that decides the value each digit carries depending on where it sits. Humans naturally count in the decimal (base‑10) system because we have ten fingers, but a computer is built from switches that are either ON or OFF — so at heart it can only store two states: 1 and 0. This is why the binary (base‑2) system is the true language of every CPU, memory chip and storage device.
For Bangladeshi government job exams (BCS, Bank AD/Officer‑IT, NTRCA, and PSC IT‑officer posts), this topic is a guaranteed source of marks. Questions ask you to convert a number from one base to another, add or subtract in binary, read hexadecimal colour codes or memory addresses, and know facts such as "how many values can 8 bits store" or "what is the base of the octal system". If you master the method rather than memorising single answers, you can solve any variation they throw at you. This lesson builds the whole topic from first principles so that after studying it you will never fear a number‑system MCQ again.
Learning objectives
- Understand what a positional number system is and what "base" (radix) means.
- Know the four systems used in computing: decimal, binary, octal, hexadecimal — their digits and everyday use.
- Convert confidently in every direction: any base → decimal, decimal → any base, and the fast binary ↔ octal ↔ hexadecimal shortcuts.
- Convert fractional numbers (numbers with a point) between bases.
- Perform binary arithmetic: addition, subtraction, and subtraction using 1's and 2's complement.
- Represent signed numbers and understand ranges (e.g. how far 8 bits reach).
- Avoid the classic exam traps and answer factual MCQs (bits, bytes, nibble, BCD, etc.).