Number System

Number system

When we type some letters or words, the computer translates it into numbers as computers can only understand numbers. The computer is able to understand positional numeration system where there are only a couple of symbols called digits and these symbols represent different values counting on the position they occupy in the number.

A value of every digit during a number are often determined using

 The digit

 The position of the digit in the number

The base of the number system is defined as the total number of digits available in the number system.

Decimal Number System

The numeration system that we use in our day-to-day life is that the decimal number system. Decimal numeration system has base 10 because it uses 10 digits from 0 to 9. In decimal numeration system , the successive positions to the left of the percentage point represent units, tens, hundreds, thousands then on.

Each position represents a selected power of the bottom (10). suppose in the decimal number 1234 consists of the  digit 4 within the units position, 3 within the tens position, 2 within the hundreds position, and 1 within the thousands position, and its value are often written as

(1x1000)+ (2x100)+(3x10)+ (4xl)

(1x103)+ (2x102)+ (3x101)+ (4xl00)

1000 + 200 + 30 + 4

1234

.

S.N. Number System and Description

1. Binary Number System

Base 2. Digits used : 0, 1

2. Octal Number System

Base 8. Digits used : 0 to 7

3. Hexa Decimal Number System

Base 16: Digits are used: 0 to 9, Letters are used : A- F

Binary Number System

Characteristics of binary number system are as follows:

Uses two digits, 0 and 1. Also called base 2 number system

Example

Binary Number: 10101

Calculating Decimal Equivalent:

Step Binary Number Decimal Number

Step 1: 10101= (1 x 2⁴) + (0 x 2³) + (1 x 2²) + (0 x 2¹) + (1 x 2⁰)

Step 2:        =(16 + 0 + 4 + 0 + 1)

Step 3 =21

Octal Number System

Characteristics of octal number system are as follows:

 Uses eight digits, 0,1,2,3,4,5,6,7. Also called base 8 number system

Example

Octal Number: 125708

Calculating Decimal Equivalent:

Step Octal Number TO Decimal Number

Step 1: 125708=((1 x 8⁴) + (2 x 8³) + (5 x 8²) + (7 x 8¹) + (0 x 8⁰)

Step 2: = (4096 + 1024 + 320 + 56 + 0)

Step 3: =549610

Hexadecimal Number System

Characteristics of hexadecimal number system are as follows:

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.

Here A = 10. B = 11, C = 12, D = 13, E = 14, F = 15. It is also called base 16 number system

Example

Hexadecimal Number: FDE

Calculating Hexadecimal TO Decimal:

STEP1: FDE=15X16³+13X16²+14X16¹

STEP2: =61440+3328+224

STEP3: =64992

video tutorial of number system