Converting binary into decimal (denary) is very simple and can be done by simply remembering the following numbers:
128, 64, 32, 16, 8, 4, 2, 1
Have you noticed anything about these numbers?
From right to left they are doubling every time!
So why do we need to remember these numbers?
Let me show you with 2 examples.
Example 1.
Convert 10001101 into denary.
All we need to do to convert this binary number is draw out a table. Put the numbers, 128, 64, 32 etc from above into the top row and our binary number into the bottom row:
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
| 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 |
All we need to do is add up all the numbers on the top row if there is a 1 underneath it:
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
| 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 |
| 128 + | 0 | 0 | 0 | 8 + | 4 + | 0 | 1 |
We work out 128 + 8 + 4 + 1 = 141
The binary number 10001101 = 141 in denary.
Example 2.
Convert 10101010 into decimal.
We draw out our table and put the binary number underneath it.
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
| 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 |
We then add up all the numbers on the top row if there is a 1 underneath it:
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
| 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 |
| 128 + | 0 | 32 + | 0 | 8 + | 0 | 2 | 0 |
We work out 128 + 32 + 8 + 2 = 170
The binary number 10101010 = 170 in decimal.
Do I have to remember how to do this for an exam?
Yes absolutely! Conversions are a favourite question in exams and are some really easy marks. For GCSE, you will be expected to convert up to 8 digits of binary (exactly what you have been shown here).
