Binary subtraction is similar to subtracting numbers in decimal. If you are going to be working with the binary number system often then it is useful to be able to subtract binary numbers. To make it easy there are four simple rules we can remember:
However, Rule 4 is where it gets a bit tricky, here we can state:
We have to remember here that when using this rule when subtracting large binary number for each other that we might need to borrow one digit from a higher order to complete our binary subtraction.
The best way to learn how to subtract binary numbers is through some worked examples. Follow along with our two worked examples below to improve your binary subtraction skills.
In the below example we subtract 7 (111) and 2 (10) together in binary. This is an easy example as it does not include any borrowing:
In the below example we subtract 10 (1010) and 5 (111) together in binary. This is a harder example as it includes borrowing:
The below image contains some examples of binary subtraction.
Using our free binary subtraction calculator is easy. First type the first number you want to subtract from into the top input box. This will have to be in binary (so use 1s and 0s only) but the calculator will show you the converted decimal version next to the input so you can check you have converted to binary correctly. Next input the second number (the one you want added) into the bottom input box. Again this will have to be in binary but the calculator will convert this for you to decimal so you can check. Finally click calculate to get your result. Both subtracted results in both the binary and decimal will be provided. If you want to calculate more subtraction combinations then you can reset the calculator at the top left of the tool.
Like all tools on binarytables.com the binary subtraction calculator is free to use!