# 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