How Does a Computer Calculate Numbers?

By Isaiah David; Updated April 24, 2017

Binary

Computer numbers are written with ones and zeros only.

Computers turn every number into binary. The numbers that we use are expressed in base 10. Every 10 1s equals 1 ten, every 10 tens equals 1 hundred, and so on. In binary, you go up a unit every 2 numbers. So 2 ones equals 1 two, 2 twos equal 1 4, and so on. For example, the number 9 would be 1001 in binary: 1 one, 0 twos, 0 fours, and 1 eight. 1 + 8 =9. Computers do this because it is easier to design circuits that only have values of 1 or 0 than circuits with 10 separate values each.

Addition

Computers have basic mathematical operations like addition and subtraction programmed into them. Adding in binary is extremely simple. If you have 2 numbers with a 1 value, you store a 0 and move carry 1. Otherwise, you record the bigger of the two numbers in that slot. For example, if you are adding 5 + 4, you get: 0101 + 0100. In the first slot, you have a 1 + 0, so you store the bigger number, 1. In the second slot, you have two 0s, so you store 0 (since both numbers are the same. In the third slot you have two 1s, so you store a 0 and carry a 1. You end up with the number 1001, or 9.

Multiplication.

Computers use long multiplication, but they do it in binary. If the computer multiplies a number by 1, it returns a 1. This is a much simpler system than base 10, even though it does require more steps. For example, in base 10 the problem 8 * 9 is an easy, 1-step problem with no long multiplication. However, in binary each number is 4 digits long, and the solution is 7 digits long!

Subtraction

Subtraction is done in two steps. Rather than subtracting a number, a binary computer adds its compliment, a number with ones where the original has zeros, and zeros where the original has ones. For example, whereas 4 is 0100 in binary, negative 4 is 1011. So, for 7 - 4, we get 0111 + 1011 = 10010. The number at the leftmost side is then moved to the right, giving us 0011 = 3.

About the Author

Isaiah David is a freelance writer and musician living in Portland, Ore. He has over five years experience as a professional writer and has been published on various online outlets. He holds a degree in creative writing from the University of Michigan.