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.
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 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).
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 represents units, tens, hundreds, thousands and so on.
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
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.
systems which are frequently used in computers.
Binary Number System
Characteristics
· Uses two digits, 0 and 1.
· Also called 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 an x power of the base
(2). Example: 2x where x represents
the last position - 1.
the last position - 1.
Example
Binary Number: 101012
Calculating Decimal Equivalent −
Step
|
Binary Number
|
Decimal Number
|
Step 1
|
101012
|
((1 × 24)
+ (0 × 23) +(1 × 22) + (0 ×
21) + (1 × 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
· Uses eight digits, 0,1,2,3,4,5,6,7.
· Also called 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 an x power of the base
(8). Example: 8x where x represents
the last position - 1.
the last position - 1.
Example
Octal Number − 125708
Calculating Decimal Equivalent −
Step
|
Octal Number
|
Decimal Number
|
Step 1
|
125708
|
((1 × 84)
+ (2 × 83) + (5 × 82) + (7 ×
81) + (0 × 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
· 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.
· Also called 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 an x power of the
base (16). Example 16x
where x represents the last position - 1.
where x represents the last position - 1.
Example −
Hexadecimal Number: 19FDE16
Calculating Decimal Equivalent −
Step
|
Binary Number
|
Decimal Number
|
Step 1
|
19FDE16
|
((1 × 164)
+ (9 × 163) + (F × 162) + (D
× 161) + (E × 160))10
|
Step 2
|
19FDE16
|
((1 × 164)
+ (9 × 163) + (15 × 162) +
(13 × 161) + (14 × 160))10
|
Step 3
|
19FDE16
|
(65536 +
36864 + 3840 + 208 + 14)10
|
Step 4
|
19FDE16
|
10646210
|
Note − 19FDE16 is
normally written as 19FDE.
