Number Bases (AQA GCSE Computer Science): Revision Note

Decimal (Base 10)

What is decimal (base 10)?

• Decimal is a number system that is made up of 10 digits (0-9)

• Decimal is referred to as a base-10 number system

• Each digit has a weight factor of 10 raised to a power, the rightmost digit is 1s (10⁰), the next digit to the left 10s (10¹) and so on

• Humans use the denary system for counting, measuring and performing maths calculations

• Using combinations of the 10 digits we can represent any number

• In this example, (3 x 1000) + (2 x 100) + (6 x 10) + (8 x 1) = 3268

• To represent a bigger number we add more digits

Binary (Base 2)

What is binary?

• Binary is a number system that is made up of two digits (1 and 0) 

• Binary is referred to as a Base-2 number system

• Each digit has a weight factor of 2 raised to a power, the rightmost digit is 1s (2⁰), the next digit to the left 2s (2¹) and so on

• Using combinations of the 2 digits we can represent any number

• In this example, (1 x 8) + (1 x 4) = 12

• To represent bigger numbers we add more binary digits (bits)

Why do computers use binary?

• The CPU is made up of billions of tiny transistors, transistors can only be in a state of on or off

• Computers use binary numbers to represent data (1 = on, 0 = off)

Hexadecimal (Base 16)

What is hexadecimal?

• Hexadecimal is a number system that is made up of 16 digits, 10 numbers (0-9) and 6 letters (A-F)

• Hexadecimal is referred to as a Base-16 number system

• Each digit has a weight factor of 16 raised to a power, the rightmost digit is 1s (16^0), the next digit to the left 16s (16^1)

• In GCSE you are required to work with up to and including 2 digit hexadecimal values

• A quick comparison table demonstrates a relationship between hexadecimal and a binary nibble 

• One hexadecimal digit can represent four bits of binary data

Why is hexadecimal used?

• In Computer Science hexadecimal is often preferred when working with large values

• It takes fewer digits to represent a given value in hexadecimal than in binary

• It is beneficial to use hexadecimal over binary because:

  • The more bits there are in a binary number, the harder it is to read

  • Numbers with more bits are more prone to errors when being copied

• Examples of where hexadecimal can be seen:

  • MAC addresses

• Colour values