1.3 NUMBER SYSTEM

A digital system can understand positional number system only where there are only a few symbols called digits and these symbols represent different values depending on the position they occupy in the number.

 A value of each digit in a number can be determined using

• The digit
• The position of the digit in the number
• The base of the number system (where base is defined as the total number of digits available in the number system).

Base of a Number System: Base is the characteristic of a number system. It can be thought of as the number of objects grouped together in the system.

4 Types of Number Systems

Ø  Decimal Number System

Characteristics

·         Uses ten digits: 0,1,2,3,4,5,6,7,8,9.

·         Also called base 10 number system

·         Each position represents a specific power of the base (10). For example, the decimal number 1234 consists of the digit 4 in the units position, 3 in the tens position, 2 in the hundreds position, and 1 in the thousands position.

Ø  Binary Number System

Characteristics

·         Uses two digits: 0 and 1.

·         Also called base 2 number system

Ø  Octal Number System

Characteristics

·         Uses eight digits: 0,1,2,3,4,5,6,7.

·         Also called base 8 number system

Ø  Hexadecimal Number System

Characteristics

·         Uses 10 digits and 6 letters: 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F.

·         Letters represents numbers starting from 10.

A = 10, B = 11, C = 12, D = 13, E = 14, F = 15.

·         Also called base 16 number system