How to Convert Decimal Numbers to Binary

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This is a quick method to convert a decimal number into a binary number.[1]

The binary number is constructed from right to left.

  1. If the decimal number is even, write a 0. If it's odd, write a 1.
  2. Divide the number in two and round down.
  3. Again, if the decimal number is even, write a 0. If it's odd, write a 1.
  4. Keep dividing the number until you get to 1.

Example

Convert 99 to binary:

  • 99 is odd, so start with: 1
  • Divide 99 in 2 (49.5) and round down. 49 is odd, so add a 1 on the left: 11.
  • Divide 49 in 2 (24.5) and round down. 24 is even, so add a 0 on the left: 011.
  • Divide 24 in 2 (12). 12 is even, so add another 0 on the left: 0011.
  • Divide 12 in 2 (6). 6 is even, so add another 0 on the left: 00011.
  • Divide 6 in 2 (3). 3 is odd, so add a 1 on the left: 100011.
  • Divide 3 in 2 (1.5) and round down. 1 is odd, so add a 1 on the left: 1100011.

99 is 1100011 in binary.

Memorization

Since this is meant to be done in one's head, maybe the ones and zeros could be kept track of with finger positions. Keep fingers by sides or on the table in front of you, slightly off the surface. Since it's calculated from right to left, the first binary digit would be represented by your right pinky and each additional digit would move to the left. If it's a 1, put your fingertip down. If it's a 0, put your finger down, but curl the finger.

Note: this finger method was only quickly tested. If you think of a better way to keep track of the binary digits, please post in the Art of Memory Forum.

References