NUMBER SYSTEM
There are basically two types
of number systems:
1. Positional Number System
2. Non-Positional Number system.
Four types of positional
number systems are:
1)
Binary number
system
2)
Decimal number
system
3)
Octal number
system
4)
Hexadecimal
number system
|
Number system
|
Digits
|
Total digits
|
Base
|
Example
|
|
Binary
|
0 & 1
|
2
|
2
|
(101001)2
|
|
Decimal
|
0,1,2,3,4,5,6,7,8,9
|
10
|
10
|
(8579)10
|
|
Octal
|
0,1,2,3,4,5,6,7
|
8
|
8
|
(6756)8
|
|
Hexadecimal
|
0,1,2,3,4,5,6,7,8,9,10(A),
11(B),12(C),13(D),14(E),15(F)
|
16
|
16
|
(ABC9)16
|
Relationship among the
four types of number system:
|
Decimal
number
|
Binary
number
|
Octal
number
|
Hexadecimal
number
|
|
0
|
0
|
0
|
0
|
|
1
|
1
|
1
|
1
|
|
2
|
10
|
2
|
2
|
|
3
|
11
|
3
|
3
|
|
4
|
100
|
4
|
4
|
|
5
|
101
|
5
|
5
|
|
6
|
110
|
6
|
6
|
|
7
|
111
|
7
|
7
|
|
8
|
1000
|
10
|
8
|
|
9
|
1001
|
11
|
9
|
|
10
|
1010
|
12
|
A
|
|
11
|
1011
|
13
|
B
|
|
12
|
1100
|
14
|
C
|
|
13
|
1101
|
15
|
D
|
|
14
|
1110
|
16
|
E
|
|
15
|
1111
|
17
|
F
|
Conversions
1)
Conversion from
decimal to binary
Example-
(42)10, (0.8125)10
2)
Conversion from
decimal to octal
Example-
(952)10
3)
Conversion from
decimal to hexadecimal
Example-
(428)10
4)
Conversion from
binary to decimal
Example-
(1011)2
5)
Binary to octal
Example-
(010111)2
6)
Binary to
hexadecimal
Example-
(0010111)2
7)
Octal to decimal
Example-
(24)8
8)
Octal to binary
Example-
(64)8
9)
Octal to
hexadecimal
Example-
(64)8
10)
Hexadecimal to
decimal
Example-
(ABC)16
11)
Hexadecimal to
binary
Example-
(ABC)16
12)
Hexadecimal to
octal
Example-
(ABC)16
BINARY ADDITION
Formula:
0+0=0
0+1=1
1+0=1
1+1=0 and carry 1 to the next
digit.
Example:
a) (010+011)2
b)
(1001+0100)2
c)
(1010+1100)2
BINARY SUBTRACTION
Formula:
0-0=0
1-0=1
1-1=0
0-1=1 and carry 1 from the
left side digit.
Example:
a) (1110-0101)2
b)
(1010-0101)2
c)
(1010-0011)2
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