How to Calculate Binary Numbers

By William Garmany; Updated April 24, 2017
There is a way to quickly change binary to base 10 and vise versa.

Calculating binary numbers can be confusing, until you figure out the system. Most of what you learned during your academic years is base 10; binary numbers use base 2. What that means is, everytime you count numbers under base 10, you are counting from zero to nine, then starting over by adding another number in front to make 10 and so on. With base 2, you have either a zero or one, then the next place holder is another zero or one.

Create a chart with multiples of two, starting with the binary number "1," from right to left to better understand binary number placement. For example: 256 128 64 32 16 8 4 2 1

Look at the binary number and place it in your chart. If the binary number is 110100101 then you would do as follows: 256 128 64 32 16 8 4 2 1 ..1....1...0...1...0..0.1.0.1

Add up all of the numbers that have a binary "1" place holder. In the example, add 256 + 128 + 32 + 4 + 1, which gives you a result of 421. Use this number in your calculations.

Convert numbers back to binary using the same chart. For example, if you have 637 that you want to convert to binary, start with the multiple of two larger than 637, 1,024, and create your chart: 1024 512 256 128 64 32 16 8 4 2 1

Place a binary "1" in each of the numbers starting from the largest that are needed to add up to 637: 1024 512 256 128 64 32 16 8 4 2 1 ..........1................1...1......1.1.1.1

Drop the left-most binary "0" from your number, and you end up with the binary number; 1001111101 in place of 637.