# Computer - Number System

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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 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 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 2x where x represents the last position - 1.

### Example

Binary Number: 101012

Calculating Decimal Equivalent −

Step Binary Number Decimal Number
Step 1 101012 ((1 x 24) + (0 x 23) + (1 x 22) + (0 x 21) + (1 x 20))10
Step 2 101012 (16 + 0 + 4 + 0 + 1)10
Step 3 101012 2110

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 8x where x represents the last position - 1

### Example

Octal Number: 125708

Calculating Decimal Equivalent −

Step Octal Number Decimal Number
Step 1 125708 ((1 x 84) + (2 x 83) + (5 x 82) + (7 x 81) + (0 x 80))10
Step 2 125708 (4096 + 1024 + 320 + 56 + 0)10
Step 3 125708 549610

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 16x where x represents the last position - 1

### Example

Hexadecimal Number: 19FDE16

Calculating Decimal Equivalent −

Step Binary Number Decimal Number
Step 1 19FDE16 ((1 x 164) + (9 x 163) + (F x 162) + (D x 161) + (E x 160))10
Step 2 19FDE16 ((1 x 164) + (9 x 163) + (15 x 162) + (13 x 161) + (14 x 160))10
Step 3 19FDE16 (65536+ 36864 + 3840 + 208 + 14)10
Step 4 19FDE16 10646210

Note − 19FDE16 is normally written as 19FDE.

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