It looks like there are a lot of steps to convert a denary number into binary, but really you're just repeating the same step eight times.
We are going to convert 186 from denary to binary.
Step 1
Look at the 1st binary placeholder value (128).
Is 128 less than, or the same as, 186?
Yes, so we put a 1 in the 1st column.
Now we need to subtract 128 from 186 which leaves 58.This is the number we are now working with.
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
| 1 |
Step 2
Look at the 2nd binary placeholder value (64).
Is 64 less than, or the same as, 58?
No, so we put a 0 in the 2nd column, and move on to the next one.
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
| 1 | 0 |
Step 3
Look at the 3rd binary placeholder value (32).
Is 32 less than, or the same as, 58?
Yes, so we put a 1 in the 3rd column.
Now we need to subtract 32 from 58 which leaves 26.This is the number we are now working with.
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
| 1 | 0 | 1 |
Step 4
Look at the 4th binary placeholder value (16).
Is 16 less than, or the same as, 26?
Yes, so we put a 1 in the 4th column.
Now we need to subtract 16 from 26 which leaves 10.This is the number we are now working with.
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
| 1 | 0 | 1 | 1 |
Step 5
Look at the 5th binary placeholder value (8).
Is 8 less than, or the same as, 10?
Yes, so we put a 1 in the 5th column.
Now we need to subtract 8 from 10 which leaves 2.This is the number we are now working with.
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
| 1 | 0 | 1 | 1 | 1 |
Step 6
Look at the 6th binary placeholder value (4).
Is 4 less than, or the same as, 2?
No, so we put a 0 in the 6th column, and move on to the next one.
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
| 1 | 0 | 1 | 1 | 1 | 0 |
Step 7
Look at the 7th binary placeholder value (2).
Is 2 less than, or the same as, 2?
Yes, so we put a 1 in the 7th column.
Now we need to subtract 2 from 2 which leaves 0.This is the number we are now working with.
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
| 1 | 0 | 1 | 1 | 1 | 0 | 1 |
Step 8
Look at the 8th binary placeholder value (1).
Is 1 less than, or the same as, 0?
No, so we put a 0 in the 8th column. There are no more binary digits left, so we are done.
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|---|---|
| 1 | 0 | 1 | 1 | 1 | 0 | 1 | 0 |