Using binary (Edexcel GCSE Computer Science): Revision Notes

Using binary

What is binary?

Binary is a number system that uses only two digits: 1 and 0. In computing, binary is essential because it's used to represent all data and programme instructions that computers process. Every piece of information your computer handles - from text messages to videos - is ultimately stored and processed as patterns of 1s and 0s.

Why do computers use binary?

Computer processors are made up of billions of tiny electronic components called transistors. These transistors work like incredibly fast switches that can only be in one of two states:

• On (represented by 1)
• Off (represented by 0)

This is similar to a light switch in your home - it's either on or off, there's no in-between state. Because transistors can only handle these two states reliably, the binary system with its two digits (1 and 0) is perfect for computers.

Understanding the binary system

Bits, nibbles and bytes

The building blocks of binary data have specific names:

• Bit: The smallest unit of data, representing a single binary digit (1 or 0)
• Nibble: A group of 4 bits
• Byte: A group of 8 bits

These groupings allow computers to represent much more complex information than just simple on/off states. By combining multiple bits together, we can create unique patterns that represent different types of data.

How information is represented in binary

Text representation

To represent text, computers need to handle much more than just two states. Consider what's needed for basic text:

• 26 lowercase letters (a-z)
• 26 uppercase letters (A-Z)
• Punctuation marks (full stops, question marks, etc.)

Each character gets its own unique binary pattern, allowing computers to store and display text.

Graphics representation

For graphics and images, computers use binary to represent visual information. When only two digits are available, images appear in black and white with no other colours or shades possible. However, by using more bits, computers can represent millions of different colours.

Combining bits to create more possibilities

The power of binary comes from combining multiple bits together. The more bits you use, the more unique combinations you can create:

• 2 bits can create $2^2 = 4$ different combinations (00, 01, 10, 11)
• 3 bits can create $2^3 = 8$ different combinations
• 4 bits can create $2^4 = 16$ different combinations

The formula

The number of unique binary patterns that can be created with n bits is calculated using:

$\text{Number of combinations} = 2^n$

Where n is the number of bits you're using.

Place values in binary

Just like in our normal decimal system where each digit has a place value (ones, tens, hundreds), binary also uses place values. However, instead of increasing by factors of 10, binary place values increase by powers of 2.

In binary, each digit position represents a power of 2, with the rightmost digit having the lowest value. As you move left, each position has double the value of the position to its right.

Worked example: calculating colour possibilities

Exam tips

• Remember the powers of 2: $2^1=2$, $2^2=4$, $2^3=8$, $2^4=16$, $2^5=32$, $2^6=64$, $2^7=128$, $2^8=256$
• Watch for key terms: Make sure you know the difference between bits, nibbles, and bytes
• Formula questions: Always show your working when calculating combinations using $2^n$
• Real-world connections: Think about how binary limitations affect things like image quality and file sizes