Converting from denary to binary

A method of converting a denary number to binary

There is a very simple method to convert a denary number into a binary number. Let’s take the number 199.

Start by writing out the first few binary place values (128, 64, 32, 16, 8, 4, 2, 1).

1286432168421

Start at the far left point and say “Can 128 be taken away from 199?”. If it can, do that.

199 – 128 = 71. Because 128 could be taken off, put a 1 in the ‘128’ place value column:

1286432168421
1

Now repeat for 64: 71 – 64 = 7

1286432168421
11

And again for 32: 7 – 32 won’t work, so put a 0 in that place value column.

1286432168421
110

Try again for 16: 7 – 16 won’t work, so add a 0 to that place value column.

1286432168421
1100

Next is 8: 7 – 8 won’t work. Add a 0 to the ‘8’ place value column.

1286432168421
11000

Try again for 4: 7 – 4 = 3, so add a 1 to the ‘4’ place value column.

1286432168421
110001

Next try 2: 3 – 2 = 1, so add a 1 to the ‘2’ place value column.

1286432168421
1100011

And finally, 1: 1 – 1 = 0 – add a 1 to the ‘1’ place value column.

1286432168421
11000111

This means that 199 as a binary number is 1100 0111.

Note that binary numbers are usually written in blocks of four, separated by a space (eg 0111 1011). In denary, numbers are often written in blocks of three (eg 6 428 721).

A quick way to check whether your binary number is likely to be correct is by looking at the last digit. If the denary number was odd, this last binary digit should be a 1. If it was an even number this binary digit should be a 0.