## Introduction

### What is binary?

Binary is a base 2 number system, meaning that all numbers and other data can only represented using ones and zeros. All modern computer systems store data and programs in binary.

### Why do computers use binary?

There are a number of advantages to using binary in computer systems:

**Key Advantages**

- Binary data can be transmitted easily and reliably.
- Binary data can be stored and read very easily and reliably.
- Computers use circuits that can only be on one of 2 states – on or off, these work very well with binary calculations.
- The input voltage in to computers is not very stable, so only a system that use voltage/no voltage would be reliable.

Take a look at the following video for more detailed information.

*YouTube blocked at school? Watch the Google Drive version instead.*

## Bits, Bytes, Nibbles

### Bits, Bytes & Nibbles

**Bit – e.g. 0**

Each individual 1 or 0 is known as a **bit**.

Here are three bits – 110

**Byte – e.g. 11001100**

Each group of 8 bits is known as a **Byte**

Here is a** stream** of Bytes:

01010011 01101011 01111001 01110010 01101001 01101101 00100000 01101001 01110011 00100000 01100001 01110111 01100101 01110011 01101111 01101101 01100101 00100001

**Nibble – e.g. 1111**

A nibble is **4 bits**, or half a** Byte**.

Here is a nibble – 1101

## Denary to Binary

**Decimal to Binary Conversion**

Let’s suppose we are trying to find the binary for the **decimal number 75.**

### Step 1 – Write the 128 to 1 numbers

Starting on the right hand side, write down the numbers 1, 2,4,8 etc, doubling each time until you reach 128.

**Remember smallest number at the right hand side!!!**

### Step 2 – Cross out the unused numbers

Keeping only the numbers that you need to add up to your decimal number, cross out all other numbers.

### Step 3 – Write the ones or zeros

Under each number write a 1 if there is a number and a zero if you crossed out the number. Put the numbers all together and you have your binary number!

## Binary to Denary

**Binary to decimal Conversion**

Let’s suppose we are trying to find the decimal for the **binary number 01101011.**

### Step 1 – Write the 128 to 1 numbers

Starting on the right hand side, write down the numbers 1, 2,4,8 etc, doubling each time until you reach 128.

**Remember smallest number at the right hand side!!!**

### Step 2 – Write the ones and zeros below the numbers

### Step 3 – Add up all the numbers with 1s below them to find your decimal number

## Practice

### Practice

Practice converting denary to binary with the great little game.