Computer Number System - Computer Fundamentals

What is the number system? How many types are there?

As we know computers rules the world today, to perform any functions or tasks we need to give instructions to the computer in its own language. As computer cannot understand human language, when the user type some letters or words, the computer translates them in numbers as computers can understand only numbers i.e machine language. A computer can understand the positional number system in the form of 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 particularly 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 attains 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
A computer programmer or an IT professional 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
Note101012is 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 that starts 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
Note19FDE16is normally written as 19FDE.

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