Computers store all data as binary (base-2) - patterns of 0s and 1s.
Definition
Binary is a number system using only two digits: 0 and 1. Each digit position represents a power of 2.
Key Point
Place Values (8-bit):
| Bit position | 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
|---|---|---|---|---|---|---|---|---|
| Value (2^n) | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
Worked Example
Worked Example: Binary to Denary Conversion
Convert 10110101 to denary:
Calculation: 128 + 32 + 16 + 4 + 1 = 181
Answer: 10110101 in binary = 181 in denary
Convert 10110101 to denary:
| Value | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|---|
| Bit | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 1 |
Answer: 10110101 in binary = 181 in denary
Worked Example
Worked Example: Denary to Binary Conversion
Convert 157 to binary:
Method: Repeatedly divide by 2, note remainders.
Read remainders bottom to top: 10011101
Answer: 157 in denary = 10011101 in binary
Convert 157 to binary:
Method: Repeatedly divide by 2, note remainders.
| Division step | Quotient | Remainder |
|---|---|---|
| 157 ÷ 2 | 78 | 1 |
| 78 ÷ 2 | 39 | 0 |
| 39 ÷ 2 | 19 | 1 |
| 19 ÷ 2 | 9 | 1 |
| 9 ÷ 2 | 4 | 1 |
| 4 ÷ 2 | 2 | 0 |
| 2 ÷ 2 | 1 | 0 |
| 1 ÷ 2 | 0 | 1 |
Answer: 157 in denary = 10011101 in binary