Computer number system

Computer - Number System

When we type some letters or words, the computer translates them in numbers as computers can understand only numbers. A computer can understand the positional number system where there are only a few symbols called digits and these symbols represent different values depending on the position they occupy in the number.

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

Decimal Number System

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

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. Its value can be written as

(1 x 1000)+ (2 x 100)+ (3 x 10)+ (4 x l) (1 x 10³)+ (2 x 10²)+ (3 x 10¹)+ (4 x l0⁰) 1000 + 200 + 30 + 4 1234

As a computer programmer or an IT professional, you should understand the following number systems which are frequently used in computers.

S.No.Number System and Description1

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 used: 0 to 9, Letters used : A- F

Binary Number System

Characteristics of the binary number system are as follows −

Uses two digits, 0 and 1

Also called as base 2 number system

Each position in a binary number represents a 0 power of the base (2). Example 2⁰

Last position in a binary number represents a x power of the base (2). Example 2^x where x represents the last position - 1.

Example

Binary Number: 10101₂

Calculating Decimal Equivalent −

StepBinary NumberDecimal NumberStep 110101₂((1 x 2⁴) + (0 x 2³) + (1 x 2²) + (0 x 2¹) + (1 x 2⁰))₁₀Step 210101₂(16 + 0 + 4 + 0 + 1)₁₀Step 310101₂21₁₀

Note − 10101₂ is normally written as 10101.

Octal Number System

Characteristics of the octal number system are as follows −

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

Also called as base 8 number system

Each position in an octal number represents a 0 power of the base (8). Example 8⁰

Last position in an octal number represents a x power of the base (8). Example 8^x where x represents the last position - 1

Example

Octal Number: 12570₈

Calculating Decimal Equivalent −

StepOctal NumberDecimal NumberStep 112570₈((1 x 8⁴) + (2 x 8³) + (5 x 8²) + (7 x 8¹) + (0 x 8⁰))₁₀Step 212570₈(4096 + 1024 + 320 + 56 + 0)₁₀Step 312570₈5496₁₀

Note − 12570₈ is normally written as 12570.

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 represent the numbers starting from 10. A = 10. B = 11, C = 12, D = 13, E = 14, F = 15

Also called as base 16 number system

Each position in a hexadecimal number represents a 0 power of the base (16). Example, 16⁰

Last position in a hexadecimal number represents a x power of the base (16). Example 16^x where x represents the last position - 1

Example

Hexadecimal Number: 19FDE₁₆

Calculating Decimal Equivalent −

StepBinary NumberDecimal NumberStep 119FDE₁₆((1 x 16⁴) + (9 x 16³) + (F x 16²) + (D x 16¹) + (E x 16⁰))₁₀Step 219FDE₁₆((1 x 16⁴) + (9 x 16³) + (15 x 16²) + (13 x 16¹) + (14 x 16⁰))₁₀Step 319FDE₁₆(65536+ 36864 + 3840 + 208 + 14)₁₀Step 419FDE₁₆106462₁₀

Note − 19FDE₁₆ is normally written as 19FDE.