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## Notes > Foundations of Computing > Number Systems

A number system is a set of rules and symbols used to represent a number. There are several different number systems. Some examples of number systems are as follows:

• Binary (base 2)
• Decimal (base 10)
• Hexidecimal (base 16)
Decimal and Hexidecimal numbers can each be represented using binary. This enables decimal, hexidecimal, and other number systems to be represented on a computer which is based around binary (0 or 1 / off or on).

The base (or radix) of a number system is the number of units that is equivalent to a single unit in the next higher counting space. In the decimal number system, the symbols 0-9 are used in combination to represent a number of any size. For example, the number 423 can be viewed as the following string of calculations:

(4 x 100) + (2 x 10) + (3 x 1) = 400 + 20 + 3 = 423

It is important to note why binary numbers are used in computers and why, for example, the decimal number system is not used as the standard number system. Firstly, all number systems can be derived from binary therefore it is appropriate for a computer system which will have to deal with many different number systems.

A bit can have one of two values (0 or 1) and any physical medium capable of switching between two states (such as a transistor) may be used to represent a bit. A computer's circuitry involves voltage signals which have different levels (low or high) that represent a binary 0 or 1. A transistor can therefore be used as a physical representation of a bit. An elementary building block for a computer therefore is a transistor.

An example of binary representation:

The word "DAD" is represented by the bits contained in three bytes as follows: 00000100 00000001 00000100
The word "DAD" is typed into the computer system using an external input device (such as a keyboard) then this is stored temporarily in memory as a string of bits while it is being displayed on an external output device (Visual Display Unit).

Switching Theory forms the mathematical foundation for digital circuits. Switching Theory concentrates on switching functions that describe in/output relationships typically in digital circuits.

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