Decimal to Binary

There are several methods available to convert from base 10 to base 2. Let’s use two methods, division and subtraction, to convert the number 14110 to base 2. (Note the use of the subscript 10 (14110) to denote the base used for the number.)

The Division Method uses the remainder when successively dividing by two to convert the number. For example:

  1. 141 divided by 2 is 70 remainder 1
  2. 70 divided by 2 is 35 remainder 0
  3. 35 divided by 2 is 17 remainder 1
  4. 17 divided by 2 is 8 remainder 1
  5. 8 divided by 2 is 4 remainder 0
  6. 4 divided by 2 is 2 remainder 0
  7. 2 divided by 2 is 1 remainder 0
  8. 1 divided by 2 is 0 remainder 1

We can then write down our new binary number simply by taking each remainder reading from the bottom up, so 14110 is 100011012

We can check this using our Base 2 table:

100011012 is 128 + 8 + 4 + 1 = 14110.

Decimal to Binary: What is 169 in base 2 (binary)? Show

As you become more comfortable with the values of each binary column you can use the Subtraction Method.

  1. 141 contains one 128 leaving 13
  2. 13 contains no 64s
  3. 13 contains no 32s
  4. 13 contains no 16s
  5. 13 contains one 8 leaving 5
  6. 5 contains one 4 leaving 1
  7. 1 contains no 2s
  8. 1 contains one 1 leaving 0

We can then write this down as before as 100011012.

Next: Binary to Decimal