Digital Number System

A digital system can understand positional number system only where there are 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 digit
The position of the digit in the number
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).
The base of the number system (where base is defined as the total number of digits available in the 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 represents 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
(1×1000) + (2×100) + (3×10) + (4×l)
(1×103) + (2×102) + (3×101)  + (4×l00)
1000 + 200 + 30 + 1
1234

As a computer programmer or an IT professional, you should understand the following number systems which are frequently used in computers.
Base 2. Digits used: 0, 1
Base 8. Digits used: 0 to 7
Base 16. Digits used: 0 to 9, Letters used: A- F
Characteristics
Uses two digits, 0 and 1.
Uses two digits, 0 and 1.
Also called base 2 number system
Also called base 2 number system
Each position in a binary number represents a 0 power of the base (2). Example: 20
Each position in a binary number represents a 0 power of the base (2). Example: 20
Last position in a binary number represents an x power of the base (2). Example: 2x where x represents the last position - 1.
Last position in a binary number represents an x power of the base (2). Example: 2x where x represents the last position - 1.
Binary Number: 101012
Calculating Decimal Equivalent −
Note: 101012 is normally written as 10101.
Characteristics
Uses eight digits, 0,1,2,3,4,5,6,7.
Uses eight digits, 0,1,2,3,4,5,6,7.
Also called base 8 number system
Also called base 8 number system
Each position in an octal number represents a 0 power of the base (8). Example: 80
Each position in an octal number represents a 0 power of the base (8). Example: 80
Last position in an octal number represents an x power of the base (8). Example: 8x where x represents the last position - 1.
Last position in an octal number represents an x power of the base (8). Example: 8x where x represents the last position - 1.
Octal Number − 125708
Calculating Decimal Equivalent −
Note: 125708 is normally written as 12570.
Characteristics
Uses 10 digits and 6 letters, 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F.
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.
Letters represents numbers starting from 10. A = 10, B = 11, C = 12, D = 13, E = 14, F = 15.
Also called base 16 number system.
Also called base 16 number system.
Each position in a hexadecimal number represents a 0 power of the base (16). Example 160.
Each position in a hexadecimal number represents a 0 power of the base (16). Example 160.
Last position in a hexadecimal number represents an x power of the base (16). Example 16x where x represents the last position - 1.
Last position in a hexadecimal number represents an x power of the base (16). Example 16x where x represents the last position - 1.
Hexadecimal Number: 19FDE16
Calculating Decimal Equivalent −
Note − 19FDE16 is normally written as 19FDE.

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