Binary Number System
beginner20 minLearning objectives
- Explain why computers use binary
- Convert accurately between binary and denary
- Interpret binary values using place value
- Apply binary representation to computing scenarios
Learn
AQA 4.5.1 — Binary
Retrieval: Sequence 6 asked you to think computationally about abstraction and problem-solving in general terms - this sequence grounds that in a very concrete question computer scientists actually face: how does a machine that only has "on" and "off" represent a number at all?
Computers store everything as electrical signals that are either on or off — represented as 1 and 0. Binary (base 2) is the natural number system for digital hardware.
Denary to binary
To convert 156 to binary, repeatedly divide by 2 and record the remainders, reading bottom-to-top:
156 ÷ 2 = 78 r 0
78 ÷ 2 = 39 r 0
39 ÷ 2 = 19 r 1
19 ÷ 2 = 9 r 1
9 ÷ 2 = 4 r 1
4 ÷ 2 = 2 r 0
2 ÷ 2 = 1 r 0
1 ÷ 2 = 0 r 1
Reading remainders bottom-to-top: 10011100.
Binary to denary — place value
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
| 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 |
128 + 16 + 8 + 4 = 156 ✓ — confirms the conversion above.
Challenge
Convert 203 to binary by hand (show your working), then convert your binary answer back to denary to check it.