Computers use the binary number system — also called Base 2. Unlike our everyday decimal system (Base 10) which uses digits 0–9, binary only uses two digits: 0 and 1.
Each binary digit is called a bit. A group of 8 bits is called a byte.
When asked "why do computers use binary?", always mention that electronic components have two states — on and off — which map directly to 1 and 0.
Each position in a binary number has a place value — a power of 2. Starting from the right:
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
| 2⁷ | 2⁶ | 2⁵ | 2⁴ | 2³ | 2² | 2¹ | 2⁰ |
To convert binary to denary (decimal), add up the place values where there is a 1.
Example: Convert 10110101 to denary
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
| 1 | 0 | 1 | 1 | 0 | 1 | 0 | 1 |
128 + 32 + 16 + 4 + 1 = 181
Always show your working in the exam — write out the place value table and circle the 1s. Even if your final answer is wrong, you can still gain method marks.
To convert a denary number to binary, work from the largest place value downwards. Ask: "Does this place value fit into the number?"
Example: Convert 75 to binary
128 → No (75 < 128) → 0
64 → Yes (75 − 64 = 11) → 1
32 → No (11 < 32) → 0
16 → No (11 < 16) → 0
8 → Yes (11 − 8 = 3) → 1
4 → No (3 < 4) → 0
2 → Yes (3 − 2 = 1) → 1
1 → Yes (1 − 1 = 0) → 1
Result: 01001011
Remember to pad your answer to 8 bits with leading zeros if needed. "1001011" should be written as "01001011".
Binary addition follows four simple rules:
Example: 00110101 + 00011010
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
| 0 | 0 | 1 | 1 | 0 | 1 | 0 | 1 |
| 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 |
| 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 |
Answer: 01001111 = 79 in denary
If your binary addition produces a 9th bit (overflow), note this in your answer — examiners may specifically ask about overflow errors.
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