Computer Number System
Computer Number
System
Number
System is representation for a given number. Basically number system is of four
type.
1. Decimal Number
System
2. Binary Number System
3. Octal Number System
4. Hexadecimal Number
System
1. Decimal
Number System: The
decimal number system is the most commonly and widely used number system. The
decimal number is represented by using any one or combination of either of
these digits : 0, 1, 2, 3, 4, 5, 6, 7, 8
and 9.Since there are ten digits in this , we can say that the decimal number
system has a base or radix of 10. In this number system, numbers greater than 9
are represented by respectively using any of these digits.
4, 29, 315, 2179 are some of decimal
numbers. We can also write them as (4)10, (29)10, (315)10,
and (2179)10 respectively. Here, the subscript 10 indicates that
these numbers are decimal numbers.
Each digit in a number has a position or
place value for each of its digits. For example, (2179)10 can be
expanded as
(2179)10
= (2*103) + (1*102) + (7*101) + (9*100)
Here 2, 1,
7 and 9 are the coefficients of the appropriate power of ten i.e. 103,
102, 101 and 100.
2. Binary
Number System:
Binary numbers are used extensively in all digits systems because of the very
nature of electronics. These numbers are represented using the binary number
system. The binary number system is the second most popular system of numbers.
Any number in this number system can be represented by using 0 or 1 or any
combination of these. Since this number system has only two members so we can
say that the binary number system has a base or radix of 2.
1, 10, 101,
1110, 10110, are some examples of binary numbers. We can also write them as (1)2,
(10)2, (101)2, (1110)2 and (10110)2
respectively. Here subscript 2 indicates that these numbers are binary numbers having
base 2.
Like decimal numbers, the binary numbers can
also be expanded but instead of multiplying each digit by appropriate power of
10. We multiply each digit by appropriate power of 2. For example, (10110)2
can be expanded as,
(10110)2
= (1*24) + (0*23) + (1*22) + (1*21)
+ (1*20)
=(1*16) + (0*8) + (1*4) + (1*2)
+ (0*1)
=16 + 0 + 4 + 2 + 0
=(22)10
Thus to
convert a binary number into a decimal number we multiply each digit by
appropriate power of 2.
3. Octal
Number System: The
octal number system consists of numbers that can either to be one of eight
digits (0, 1, 2, 3, 4, 5, 6. 7) or a combination of these. Since octal numbers
can be made eight digits so we can say that octal number system has a base or
radix of 8.
2, 7, 36, 5132 are some examples of octal
numbers. We can also write them as (2)8, (7)8, (36)8,
(5132)8 respectively. Here the subscript 8 indicates that these
numbers are octal numbers. 59, 7821 are examples of invalid octal numbers as
they are made of digits other than the ones between 0 to 7.
Like decimal numbers , the octal numbers
can also be expanded but instead of multiplying each digit by appropriate power
of 10, we multiply each digit by appropriate power of 8. For example, (2312)8
can be expanded as
(2312)8
= (2*83) + (3*82) + (1*81) + (2*80)
= (2*512) + (3*64) + (1*8) +
(2*1)
= 1024 + 192 + 8 + 2
= (1226)10
Thus to
convert an octal number into a decimal number we multiply each digit by
appropriate power of 8.
4. Hexadecimal
Number System: The
Hexadecimal number system was born out of the need to express large binary
numbers concisely. It is by far the most commonly used number system in
computer literature.
The hexadecimal number system user sixteen
different digits. Because a single character must represent digits, letters are
chosen to represent values greater than 9. The sixteen that are used and
hexadecimal digits are,
0, 1, 2, 3,
4, 5, 6, 7, 8, 9, A, B, C, D, E and F.
Since sixteen digits can be used to make
hexadecimal number, so we can say that the hexadecimal number system has a base
or radix of 16.
1, 7, 23, F, 3AB, ABC5, E52A are some
examples of hexadecimal numbers. We can also write them as (1)16, (7)16,
(23)16, (F)16, (3AB)16, (ABC5)16
and (E52A)16 . The subscript
16 indicates that these numbers are hexadecimal numbers. The numbers ABP2, 23GF
are examples of invalid hexadecimal numbers because they are made of digits
that are not in the range of valid hexadecimal digits.
Hexadecimal numbers can also be expanded
like any other numbers. While expanding, we multiply each digit by appropriate
power of 16. For example, (3A9)16 can be expanded as
(3A9)16
= (3*162) + (A*161) + (9*60)
= (3*256) + (A*16) + (9*1)
= 768 + 160 + 9
= (937)10
|
Decimal Number
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
|
Binary Number
00000
00001
00010
00011
00100
00101
00110
00111
01000
01001
01010
01011
01100
01101
01110
|
Octal Number
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
|
Hexadecimal Number
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
|
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