Converting from binary to denary
Understanding denary
People use the The number system most commonly used by people. It contains 10 unique digits 0 to 9. Also known as decimal or base 10. (or decimal) number system in their day-to-day lives. This system has 10 digits that we can use: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
The value of each The value of the place, or position, of a digit in a number. is calculated by multiplying by 10 (ie by the power of 10). The first few place values look like this:
| Thousands | Hundreds | Tens | Units |
| (1000s) | (100s) | (10s) | (1s) |
| Thousands | (1000s) |
|---|---|
| Hundreds | (100s) |
| Tens | (10s) |
| Units | (1s) |
Working out the value of 1024
| Thousands (1000s) | Hundreds (100s) | Tens (10s) | Units (1s) |
| 1 | 0 | 2 | 4 |
| 1 脳 1000 + | 0 脳 100 + | 2 脳 10 + | 4 脳 1 |
| Thousands (1000s) | 1 |
|---|---|
| Hundreds (100s) | 0 |
| Tens (10s) | 2 |
| Units (1s) | 4 |
| Thousands (1000s) | 1 脳 1000 + |
|---|---|
| Hundreds (100s) | 0 脳 100 + |
| Tens (10s) | 2 脳 10 + |
| Units (1s) | 4 脳 1 |
Converting from binary to denary
To convert a A number system that contains two symbols, 0 and 1. Also known as base 2. number to denary, start by writing out the binary place values. In denary, the place values are 1, 10, 100, 1000, etc 鈥 each place value is 10 times bigger than the last. In binary, each place value is 2 times bigger than the last (ie increased by the power of 2). The first few binary place values look like this:
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
| 128 |
| 64 |
| 32 |
| 16 |
| 8 |
| 4 |
| 2 |
| 1 |
Working out the value of 1010 1000:
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
| 1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 |
| 1脳128 + | 0脳64 + | 1脳32 + | 0脳16 + | 1脳8 + | 0脳4 + | 0脳2 + | 0脳1 |
| 128 + | 0 + | 32 + | 0 + | 8 + | 0 + | 0 + | 0 |
| 128 | 1 |
|---|---|
| 64 | 0 |
| 32 | 1 |
| 16 | 0 |
| 8 | 1 |
| 4 | 0 |
| 2 | 0 |
| 1 | 0 |
| 128 | 1脳128 + |
|---|---|
| 64 | 0脳64 + |
| 32 | 1脳32 + |
| 16 | 0脳16 + |
| 8 | 1脳8 + |
| 4 | 0脳4 + |
| 2 | 0脳2 + |
| 1 | 0脳1 |
| 128 | 128 + |
|---|---|
| 64 | 0 + |
| 32 | 32 + |
| 16 | 0 + |
| 8 | 8 + |
| 4 | 0 + |
| 2 | 0 + |
| 1 | 0 |
So 1010 1000 in binary is equal to 168 in denary.