How to Subtract Binary Numbers

For those that work in the field of computers and the designing of them it is important to understand and be able to work in the binary number system. Unlike the decimal system that we all know and learned in school, the binary number system only uses the numerals zero and one. One of the basic ways to manipulate these numbers is through subtraction.

Instructions

Difficulty: Moderately Easy

1. Examine the subtraction problem that you must solve. Remember from grade school that a positive number subtracted from another positive number is the same as a negative number added to a positive number, then we can restructure the subtraction problem as an addition problem. This is called subtraction by the two's complement method.
2. Convert the number subtracted from the first number to its negative form, taking the one's complement of the number. To do this you must exchange all the ones in the number for zeroes and all zeroes for ones.
3. Add one to the ones complement you did in step two, forming the two’s complement. Now you have restructured the subtraction problem to an addition problem.
4. Take the original number and add it to the two's compliment of the second number as you would in any other addition problem in binary. Be mindful of the carries in each column of the addition problem.
5. Discard any carry bit that extends beyond the number of bit of the original or two's complement. You now have the answer to the problem of the second number subtracted from the first number.