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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 17 from denary to binary.

Step 1

Look at the 1st binary placeholder value (128).
Is 128 less than, or the same as, 17?

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, 17?

No, so we put a 0 in the 2nd column, and move on to the next one.

1286432168421
00      

Step 3

Look at the 3rd binary placeholder value (32).
Is 32 less than, or the same as, 17?

No, so we put a 0 in the 3rd column, and move on to the next one.

1286432168421
000     

Step 4

Look at the 4th binary placeholder value (16).
Is 16 less than, or the same as, 17?

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

Now we need to subtract 16 from 17 which leaves 1.This is the number we are now working with.

1286432168421
0001    

Step 5

Look at the 5th binary placeholder value (8).
Is 8 less than, or the same as, 1?

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

1286432168421
00010   

Step 6

Look at the 6th binary placeholder value (4).
Is 4 less than, or the same as, 1?

No, so we put a 0 in the 6th column, and move on to the next one.

1286432168421
000100  

Step 7

Look at the 7th binary placeholder value (2).
Is 2 less than, or the same as, 1?

No, so we put a 0 in the 7th column, and move on to the next one.

1286432168421
0001000 

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
00010001

The answer

17 in denary is equivalent to 00010001 in binary


Quick Quiz

Click the purple circle to select your answer

Convert 154 from denary to binary

10011010
00001010
10110000
01011001