# TYPES OF NUMBER SYSTEM

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## Presentation Transcript

### PRESENTATION ON NUMBER SYSTEM :

PRESENTATION ON NUMBER SYSTEM

### TYPES OF NUMBER SYSTEM :

There are two types of number systems:-     => Positional number systems     => Non positional number system TYPES OF NUMBER SYSTEM

### Non Positional Number Systems :

Characteristics:- => Use symbols such as I for 1, II for 2, III for 3,IIII for 4, etc. => Each symbol represents the same value regardless of its position in the number system. => The symbols are simply added to find out the value of the number concerned. Non Positional Number Systems

### POSITIONAL NUMBER SYSTEM :

Characteristics:-    =>This system uses only a few symbols called digits.   => These symbols represent different values depending upon the position they occupy in the number.   =>The maximum value of a single digit is equal to one less than the value of base. POSITIONAL NUMBER SYSTEM

### COMMON NUMBER SYSTEMS :

COMMON NUMBER SYSTEMS

### Decimal Number System :

Characteristics:- => It is a positional number system. => It has 10 symbols or digits(0-9).   => The maximum value of a single digit is 9. Decimal Number System

### Binary Number System :

Characteristics:-   => It is a positional number system. => It has only two symbols or digits. =>The maximum value of a single digit is 1.   . Binary Number System

### EXAMPLE OF BINARY SYSTEM :

Ex:- 101012 => (1 x 24) + (0 x 23) + (1 x 22) + (0 x 21) x (1 x 20)   => 16 + 0 + 4 + 0 + 1 => 2110 EXAMPLE OF BINARY SYSTEM

### Octal Number System :

Characteristics :-   => It is a positional number system.    => It has 8 symbols or digits. => The maximum value of a single digit is 7. Octal Number System

### EXAMPLE OF OCTAL NUMBER SYSTEM :

Ex:- 20578 => (2 x 83) + (0 x 82) + (5 x 81) + (7 x 80) => 1024 + 0 + 40 + 7 => 107110 EXAMPLE OF OCTAL NUMBER SYSTEM

Characteristics:-   =>It is a positional number system.    =>It has total 16 numbers or digits.    =>The symbols A,B,C,D,E,F represent the decimal values 10,11,12,13,14,15 respectively.    =>The maximum value of a single digit is 15. Hexadecimal Number System

### EXAMPLE FOR HEXADECIMAL SYSTEM :

Ex:- 1AF16 => (1 x 162) +(A x 161) + (F x 160) =>1 x 256 + 10 x 16 + 15 x 1 => 256 + 160 + 15 => 43110 EXAMPLE FOR HEXADECIMAL SYSTEM

### Conversion of Number Systems :

=> Converting Binary to Decimal   => Converting Hex to Decimal  => Converting Decimal to Binary   => Converting Decimal to Hex Conversion of Number Systems

### Converting Binary to Decimal :

EX:-   (101001)2 to ( )10   (1 x 25) + (0 x 24) + (1 x 23) + (0 x 22) +(0 x 21) + (1 x 20)   => 32 + 0 + 8 + 0 + 0 + 1 => (41)10 Converting Binary to Decimal

DECIMAL TO HEXADECIMAL 123410 = ?16 123410 = 4D216

### Converting Hexadecimal to Decimal :

Ex:- (A3F)16 to ( )10   => (A x 162) + (3 x 161) + (F x 160 )   => (10 x 256) + (3 x 16) + (15 x 1)   => 262310 Converting Hexadecimal to Decimal