Number System and its Conversion

NUMBER SYSTEM

Number systems are the technique to represent numbers. You may have also seen some people telling it numeral system. It can be defined as a system of writing to express numbers. It is the mathematical notation for representing numbers of a given set by using digits or other numeral symbols.

Generally we study and talk about following four number systems. While there are many others too. Here we are discussing about

Binary number system
Octal number system
Decimal number system
Hexadecimal (hex) number system

A. BINARY NUMBER SYSTEM

A Binary number system has only two digits that are 0 and 1. Every number (value) represents with 0 and 1 in this number system. The base of binary number system is 2, because it has only two digits.

B. OCTAL NUMBER SYSTEM

Octal number system has only eight (8) digits from 0 to 7. Every number (value) represents with 0,1,2,3,4,5,6 and 7 in this number system. The base of octal number system is 8, because it has only 8 digits.

C. DECIMAL NUMBER SYSTEM

Decimal number system has only ten (10) digits from 0 to 9. Every number (value) represents with 0,1,2,3,4,5,6, 7,8 and 9 in this number system. The base of decimal number system is 10, because it has only 10 digits.

D. HEXADECIMAL NUMBER SYSTEM

A Hexadecimal number system has sixteen (16) alphanumeric values from 0 to 9 and A to F. Every number (value) represents with 0,1,2,3,4,5,6, 7,8,9,A,B,C,D,E and F in this number system. The base of hexadecimal number system is 16, because it has 16 alphanumeric values. Here A is 10, B is 11, C is 12, D is 14, E is 15 and F is 16.

You can take the following tabular diagram as a cheat sheet to understand the basic and difference about number systems.

Number System	Base (Radix)	Used digits / symbols	Examples
Binary	2	0 and 1	(10001001)2
Octal	8	0,1,2,3,4.5.6.7	(3452)8
Decimal	10	0,1,2,3,...,9	(97832)10
Hexadecimal	16	0,1,2,3,...,9, A, B, C, D, E. F	(A23C87)16