Computer - Number System
Decimal Number System
Binary Number System
Example
Octal Number System
Example
Hexadecimal Number
System
Example
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.
