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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 167 from denary to binary.

Step 1

Look at the 1st binary placeholder value (128).
Is 128 less than, or the same as, 167?

Yes, so we put a 1 in the 1st column.

Now we need to subtract 128 from 167 which leaves 39.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, 39?

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, 39?

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

Now we need to subtract 32 from 39 which leaves 7.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, 7?

No, so we put a 0 in the 4th column, and move on to the next one.

1286432168421
1010    

Step 5

Look at the 5th binary placeholder value (8).
Is 8 less than, or the same as, 7?

No, so we put a 0 in the 5th column, and move on to the next one.

1286432168421
10100   

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
101001  

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
1010011 

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
10100111

The answer

167 in denary is equivalent to 10100111 in binary


Quick Quiz

Click the purple circle to select your answer

Convert 186 from denary to binary

00110001
10111010
00010110
00100011