Data representation. Number systems
Number systems
Learners should be able to…
- convert a number from one number system to another
- explain the advantages of using hexadecimal numbers in computer systems
- perform the arithmetic operations of addition and multiplication on binary numbers
Number systems
A numbering system is a way of representing numbers. The most commonly used numbering system in real life is Decimal number system. Other number systems are Binary, Hexadecimal number system. Each number system is uniquely identified by its base value or radix.
Conversion Rules of Number Systems
Why use hexadecimal?
Conversion of Decimal Number System to Binary/ Hexadecimal Number System
To convert a number from the decimal number system to a binary/hexadecimal number system, we use the following steps:
- Identify the base of the required number
- Divide the given number by the base of the required number and note down the quotient and the remainder in the quotient-remainder form. Repeat this process (dividing the quotient again by the base) until we get the quotient less than the base
Example:
Convert 700 from denary into the hexadecimal system
Thus, 700 in denary = 2BC in hexadecimal
- Hexadecimal is useful because it is much more readable to humans than binary, but at the same time it still shares a lot of the qualities of binary. It is widely used in computing because it is a much shorter way of representing a “byte” of data (8 binary digits or bits)
- To determine memory location. Hexadecimals can characterise every byte as two hexadecimal digits only compared to eight digits when using binary
- To define colors on web pages and in programming language (eg. Python). Each primary color – red, green and blue is characterised by two hexadecimal digits. The format being used is #RRGGBB. RR stands for red, GG stands for green and BB stands for blue
- To represent MAC addresses. Media Access Control addresses consist of 12-digit hexadecimal numbers. For example, 00:A0:C9:14:C8:29
- To display error messages. Hexadecimals are used to define the memory location of the error. This is useful for programmers in finding and fixing errors.