ComputingRevision.net

Converting Denary to Binary

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.

1286432168421
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.

1286432168421
10      

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.

1286432168421
101     

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.

1286432168421
1011    

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.

1286432168421
10111   

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.

1286432168421
101110  

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.

1286432168421
1011101 

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.

1286432168421
10111010

The answer

186 in denary is equivalent to 10111010 in binary


Quick Quiz

Click the purple circle to select your answer

Convert 211 from denary to binary

10011000
11010011
10001110
00111110