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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 224 from denary to binary.

Step 1

Look at the 1st binary placeholder value (128).
Is 128 less than, or the same as, 224?

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

Now we need to subtract 128 from 224 which leaves 96.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, 96?

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

Now we need to subtract 64 from 96 which leaves 32.This is the number we are now working with.

1286432168421
11      

Step 3

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

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

Now we need to subtract 32 from 32 which leaves 0.This is the number we are now working with.

1286432168421
111     

Step 4

Look at the 4th binary placeholder value (16).
Is 16 less than, or the same as, 0?

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

1286432168421
1110    

Step 5

Look at the 5th binary placeholder value (8).
Is 8 less than, or the same as, 0?

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

1286432168421
11100   

Step 6

Look at the 6th binary placeholder value (4).
Is 4 less than, or the same as, 0?

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

1286432168421
111000  

Step 7

Look at the 7th binary placeholder value (2).
Is 2 less than, or the same as, 0?

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

1286432168421
1110000 

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
11100000

The answer

224 in denary is equivalent to 11100000 in binary


Quick Quiz

Click the purple circle to select your answer

Convert 86 from denary to binary

10001101
11000110
01010110
00000110