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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 127 from denary to binary.

Step 1

Look at the 1st binary placeholder value (128).
Is 128 less than, or the same as, 127?

No, so we put a 0 in the 1st column, and move on to the next one.

1286432168421
0       

Step 2

Look at the 2nd binary placeholder value (64).
Is 64 less than, or the same as, 127?

Yes, so we put a 1 in the 2nd column.

Now we need to subtract 64 from 127 which leaves 63.This is the number we are now working with.

1286432168421
01      

Step 3

Look at the 3rd binary placeholder value (32).
Is 32 less than, or the same as, 63?

Yes, so we put a 1 in the 3rd column.

Now we need to subtract 32 from 63 which leaves 31.This is the number we are now working with.

1286432168421
011     

Step 4

Look at the 4th binary placeholder value (16).
Is 16 less than, or the same as, 31?

Yes, so we put a 1 in the 4th column.

Now we need to subtract 16 from 31 which leaves 15.This is the number we are now working with.

1286432168421
0111    

Step 5

Look at the 5th binary placeholder value (8).
Is 8 less than, or the same as, 15?

Yes, so we put a 1 in the 5th column.

Now we need to subtract 8 from 15 which leaves 7.This is the number we are now working with.

1286432168421
01111   

Step 6

Look at the 6th binary placeholder value (4).
Is 4 less than, or the same as, 7?

Yes, so we put a 1 in the 6th column.

Now we need to subtract 4 from 7 which leaves 3.This is the number we are now working with.

1286432168421
011111  

Step 7

Look at the 7th binary placeholder value (2).
Is 2 less than, or the same as, 3?

Yes, so we put a 1 in the 7th column.

Now we need to subtract 2 from 3 which leaves 1.This is the number we are now working with.

1286432168421
0111111 

Step 8

Look at the 8th binary placeholder value (1).
Is 1 less than, or the same as, 1?

Yes, so we put a 1 in the 8th column.

Now we need to subtract 1 from 1 which leaves 0.There are no binary digits left, so we are done.

1286432168421
01111111

The answer

127 in denary is equivalent to 01111111 in binary


Quick Quiz

Click the purple circle to select your answer

Convert 209 from denary to binary

11010001
01001111
10100100
01101001