Data representationIntegers

Binary is used to represent whole numbers so that they can be understood by the processor.

An integer:

• is a whole number
• can be a positive number or a negative number

The number 173 is an integer. It can be represented in binary as:

10101101

Binary works using a number system that is based on powers of 2. To understand why 10101101 is the same as 173 look at the following table:

When adding up all of the values that are on, the following sum is created:

128 + 32 + 8 + 4 + 1 = 173

In this example we are using 8 bits to represent a number. If we use 8 bits we can represent any number between 0 and 255.

If all of the values are off, the number is 0:

If all of the values are on, the number is 255:

128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255

Range of binary numbers

To figure out the range of numbers that can be stored with a set number of bits, use the following formula:

2ⁿ - 1

The reason for taking one away is because the integer 0 needs to be stored.

2⁸ = 256

2⁸ - 1 = 255

This means that the range of integers that can be represented using 8 bits is 0 – 255. Typically we categorise binary in groups of 8 bits (or 1 byte).