What is Binary, and Why Do Computers Use It?

Computers don’t understand words or numbers the way humans do. Modern software allows the end user to ignore this, but at the lowest levels of your computer, everything is represented by a binary electrical signal that registers in one of two states: on or off. To make sense of complicated data, your computer has to encode it in binary.

Binary is a base 2 number system. Base 2 means there are only two digits—1 and 0—which correspond to the on and off states your computer can understand. You’re probably familiar with base 10—the decimal system. Decimal makes use of ten digits that range from 0 to 9, and then wraps around to form two-digit numbers, with each digit being worth ten times more than the last (1, 10, 100, etc.). Binary is similar, with each digit being worth two times more than the last.

Counting in Binary

In binary, the first digit is worth 1 in decimal. The second digit is worth 2, the third worth 4, the fourth worth 8, and so on—doubling each time. Adding these all up gives you the number in decimal. So,

1111 (in binary) = 8 + 4 + 2 + 1 = 15 (in decimal)

Accounting for 0, this gives us 16 possible values for four binary bits. Move to 8 bits, and you have 256 possible values. This takes up a lot more space to represent, as four digits in decimal give us 10,000 possible values. It may seem like we’re going through all this trouble of reinventing our counting system just to make it clunkier, but computers understand binary much better than they understand decimal. Sure, binary takes up more space, but we’re held back by the hardware.

And for some things, like logic processing, binary is better than decimal.

There’s another base system that’s also used in programming: hexadecimal. Although computers don’t run on hexadecimal, programmers use it to represent binary addresses in a human-readable format when writing code. This is because two digits of hexadecimal can represent a whole byte, eight digits in binary. Hexadecimal uses 0-9 like decimal, and also the letters A through F to represent the additional six digits.