# How useful is the number system

## Computer number system

When we type some letters or words, the computer translates them into numbers like computers can only understand numbers. A computer can understand the position number of the 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 with

• The digit

• The position of the digit in the number

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

### Decimal number system

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

Each position represents a specific achievement from the base (10). For example, the decimal number 1234 consists of the digit 4 in units of space, 3 in the ten position, 2 in the hundreds, and 1 in the thousands, and its value as written

(1x1000) + (2x100) + (3x10) + (4xl) (1x103) + (2x102) + (3x101) + (4xl00) 1000 + 200 + 30 + 4 1234

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

S.N.Number system and description
1

Binary number system

Base 2nd digit used: 0, 1

2

Octal number system

Base 8th digit used: 0 to 7

3

Hexa decimal number system

Base 16. Digit Used: 0 to 9, Letters Used: A- F

### Characteristic of binary number system are as follows:

• Uses two digits, 0 and 1.

• Also as a base 2 number system

• Each position in a binary number has a 0 base (2) power. Example 2 0

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

### example

Binary number: 101012

Calculation of the decimal equivalent:

stepBinary numberDecimal number
Step 1101012((1 x 24) + (0x23) + (1 x 22) + (0x21) + (1 x 20))10
step 2101012(16 + 0 + 4 + 0 + 1)10
step 31010122110

Note : 101012 is usually written as 10101.

### Characteristic of octal number system are as follows:

• Uses eight digits, 0,1,2,3,4,5,6,7.

• Also as a base 8 number system

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

• Last position in an octal number represents ax performance of the base (8). Example 8 x where x represents the last position -1.

### example

Octal number: 125708

Calculation of the decimal equivalent:

stepOctal numberDecimal number
Step 1125708((1 x 84) + (2 x 83) + (5 x 82) + (7 x 81) + (0x80))10
step 2125708(4096 + 1024 + 320 + 56 + 0)10
step 3125708549610

Note : 125708 is usually written as 12570.

### Characteristic 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 a number starting from 10. A = 10. B = 11, C = 12, D = 13, E = 14, F = 15.

• Also as a base 16 number system

• Each position in a hexadecimal number represents a 0 power from the base (16). Example 16 0

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