NUMBER SYSTEMS IN COMPUTER ORGANIZATION

A number system is a set of symbols used to express quantities as the basis for counting ,determining order,comparing amounts, performing calculation and representing value.It is the set of characters and mathematical rules that are used to represent a number.

Ideally, a numeral system will :

• Represent a useful set of numbers(e.d. all whole numbers, integers, or real numbers)

• Give every number represented a unique representation (or at least a standard representation)

• Reflect the algebraic and arithmetic structure of the numbers

Base	Number System	Base	Number System
2	Binary	9	No nary
3	Ternary	10	Decimal
4	Quaternary	12	Duodecimal
5	Quinary	13	Tridecimal
6	Senary	14	Tetradecimal
7	Septenary	15	Pentradecimal
8	Octal	16	Hexadecimal

Decimal	Binary	Octal	Hexadecimal
0	0000	0	0
1	0001	1	1
2	0010	2	2
3	0011	3	3
4	0100	4	4
5	0101	5	5
6	0110	6	6
7	0111	7	7
8	1000	10	8
9	1001	11	9
10	1010	12	A
11	1011	13	B
12	1100	14	C
13	1101	15	D
14	1110	16	E
15	1111	17	F

The number system first introduced in human history for counting purpose. Different numbers for counting are represented by different symbols. Such as a single thing is counted by a symbol 1, if there are two things, the symbol will be 2, for counting three things, the symbol is 3. For four, five, six, seven, eight, nine the symbols used in decimal systems are 4, 5, 6, 7, 8 and 9 respectively. Symbol 0 (zero) means there is nothing to be counted. So, 0 ,1, 2, 3, 4, 5, 6, 7, 8, 9 are ten basic symbol used to count zero to nine. That’s why it is called decimal number system or base 10 system. But if there are more than nine things to be counted, then we do not go for another new symbol, rather we combine two or more symbols from 0 to 9 and represent the numbers which is more than nine. For representing nine + one that is ten, we use 10, for nine + two we use 11 and so on. In this way we established decimal number system.

There are several number systems that are important to computer science. Primary among them is the binary (base 2) number system. Other systems used are the octal (base 8) system and the hexadecimal or hex (base 16) system. Below is a table of values that you need to memorize.

Seeing a number written as 10 does not tell you what its value is. Its value may be ten or two or eight or sixteen depending on its base. You must be told what base you are working in!

Every number system as a set of allowable digits. The decimal system uses the digits 0-9; the binary system uses the digits 0 and 1; the octal system uses the digits 0-7; the hex system uses 0-9 and A-F.