2.4 Introduction to Binary

The Computer's Native Language: Binary

At their very core, computers are incredibly simple. They are made of billions of tiny electronic switches that can only be in one of two states: ON or OFF. Because of this physical reality, computers don't use the ten digits we are used to (0-9). They use a system with only two digits: 1 (for ON) and 0 (for OFF). This is the Binary Number System.

Bits and Bytes

These are the fundamental units of all digital information:

• A single 0 or 1 is called a Bit (short for Binary Digit). It's the smallest possible piece of data.
• A group of 8 bits is called a Byte. A byte can represent 256 different values (from 0 to 255).

How to Count in Binary

In our normal (base-10) system, each place value is 10 times bigger than the last (1s, 10s, 100s, etc.). In binary (base-2), each place value is 2 times bigger than the last.

It looks like this (reading from right to left):

... | 16s place | 8s place | 4s place | 2s place | 1s place |

To represent a number, we just put a '1' in the places we need to add up. Here's how we count to 5:

• 0 = 0
• 1 = 1 (one 1)
• 2 = 10 (one 2, zero 1s)
• 3 = 11 (one 2 + one 1)
• 4 = 100 (one 4, zero 2s, zero 1s)
• 5 = 101 (one 4 + zero 2s + one 1)

Visual Learners: Binary & Data

This concept is best understood visually. This Code.org video provides a fantastic explanation of how these simple 1s and 0s can be used to represent not just numbers, but text, images, and everything else on a computer.

Knowledge Check: Flip the Bits!

Ready to try it yourself? Use the interactive game below to practice converting numbers to binary. Your goal is to flip the bits on and off to match the target number.