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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 240 from denary to binary.

Step 1

Look at the 1st binary placeholder value (128).
Is 128 less than, or the same as, 240?

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

Now we need to subtract 128 from 240 which leaves 112.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, 112?

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

Now we need to subtract 64 from 112 which leaves 48.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, 48?

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

Now we need to subtract 32 from 48 which leaves 16.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, 16?

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

Now we need to subtract 16 from 16 which leaves 0.This is the number we are now working with.

1286432168421
1111    

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
11110   

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
111100  

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
1111000 

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
11110000

The answer

240 in denary is equivalent to 11110000 in binary


Quick Quiz

Click the purple circle to select your answer

Convert 153 from denary to binary

11101010
00111100
10011001
01110000