# Number Systems

Posted By on September 30, 2014

When we type some letters or words, the computer translates them in numbers as computers can understand only numbers. A computer can understand 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.

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).

## 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, and its value can be written as

```(1x1000)+ (2x100)+ (3x10)+ (4xl)
(1x103)+ (2x102)+ (3x101)+ (4xl00)
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.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 used : 0 to 9, Letters 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
• 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 octal number system are as follows:

• Uses eight digits, 0,1,2,3,4,5,6,7.
• Also called 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 represents numbers starting from 10. A = 10. B = 11, C = 12, D = 13, E = 14, F = 15.
• Also called 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.

#### Posted by Akash Kurup

Founder and C.E.O, World4Engineers Educationist and Entrepreneur by passion. Orator and blogger by hobby

Website: http://world4engineers.com