number-systems

Number bases

What is a number base?

• A number base is the number of different digits or symbols a number system uses to represent values

• Each place in a number represents a power of the base, starting from the right

Denary

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

• Denary 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

• 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

• Each time a new digit is added, the column value is multiplied by 2

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

• In this example, Binary 1100 = (1 x 8) + (1 x 4) = 12

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

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 (16⁰), the next digit to the left 16s (16¹)

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

• One hexadecimal digit can represent four bits of binary data