# Converting denary to binary: Method 2

There are two methods for converting a (base 10) number to (base 2). This is method two.

## Take off the biggest 2n value you can

Remove the 2n numbers from the main number and mark up the equivalent 2n column with a 1. Work through the remainders until you reach zero. When you reach zero, stop and complete the final columns with 0s.

A method of converting a denary number to binary

### Worked example: Denary number 84

First set up the columns of base 2 numbers. Then look for the highest 2n number that goes into 84.

1. Set up the columns of base 2 numbers
2. Find the highest 2n number that goes into 84. The highest 2n number is 26 = 64
3. 84 – 64 = 20. Find the highest 2n number that goes into 20. The highest 2n number is 24 = 16
4. 20 - 16 = 4. Find the highest 2n number that goes into 4. The highest 2n number is 22 = 4
5. 4 - 4 = 0
6. Mark up the columns of base 2 numbers with a 1 where the number has been the highest 2n number, or with a 0:
6432168421
1010100

Result: 84 in denary is equivalent to 1010100 in binary.

To check that this is right, convert the binary back to denary:

(1 x 64) + (0 x 32) + (1 x 16) + (0 x 8) + (1 x 4) + (0 x 2) + (0 x 1) = 84