Converting denary to binary: Method 2

There are two methods for converting a denary (base 10) number to binary (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