Number System
Basic Types of Number System
A number system is a basic symbol to represent a set of
quantities. Now, let us focus on binary, octal, decimal and hexadecimal number.
Number System Base
All number system have
a base. The maximum that can be represented on the single digit of number is
called a base.
The Types of
Number System
System
|
Base
|
Possible Digits
|
Binary
|
2
|
0 1
|
Octal
|
8
|
0 1 2 3 4 5 6 7
|
Decimal
|
10
|
0 1 2 3 4 5 6 7 8 9
|
Hexadecimal
|
16
|
0 1 2 3 4 5 6 7 8 9 A B C D E F
|
Binary Number
§
Binary number system
is defined by Leibniz in 1673 which
is today so important that every beginner in computer science has to learn this
number system.
§
Binary number is base of 2
§
Binary numbers are
based on the concept of ON(1) or OFF(0)
§
The weight structure
of binary number is:
§
Least significant bit(LSB) and Most
significant bit(MSB):
Octal Number
§ Octal number is base of 8
§ The assigned digits start from 0 to 7.
§ Octal number is base of 8
§ The assigned digits start from 0 to 7.
Examples:
278 = 2×81+7×80 =
16+7 = 23
308 = 3×81+0×80 = 24
43078 = 4×83+3×82+0×81+7×80=
2247
Decimal Number
§
Decimal numbers are the numbers in everyday
use.
§
Also known as Debary numbers.
§
Decimal number is the base of 10.
§
The assigned digits start from 0 to 9.
§
The positive and negative values are
determined by their position weight structure.
Example:
… 105 104 103 102 101 100 | 10-1 10-2 10-3 …
Hexadecimal Number
§
Hexadecimal number is base of 16.
§
The composed number starts from 0 until F.
§
Each group four binary digits
can be represented by a single
hexadecimal digit.
Number System Conversion
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