26-12-2017, 10:42 AM
NUMBER SYSTEM
*Digital Number Systems are the following
1.Decimal Number System
2.Binary Number System
3.Octal Number System
4.Hexa Decimal Number System
*Base of Decimal Number System
Ans : 10
*Digits used in decimal number system
Ans : 0,1,2,3,4,5,6,7,8,9 (0-9)
*Base of Binary Number System
Ans : 2
*Digits used in Binary Number System
Ans : 0,1
*Total number of digits in binary system
Ans : 2
*Base of Octal Number System
Ans : 8
*Numbers used in Octal Number System
Ans : 0,1,2,3,4,5,6,7 (0-7)
* Base of Hexa Decimal Number System -
Ans : 16
*Numbers used in Hexa Decimal Number System - 0-9 and A-F
*Numbers used in Hexa Decimal Number System - 0-9 and A-F
(0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F)
Decimal Binary Octal Hexadecimal
0 0000 0 0
1 0001 1 1
2 0010 2 2
3 0011 3 3
4 0100 4 4
5 0101 5 5
6 0110 6 6
7 0111 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
One’s complement of a binary number
*The one’s complement of a binary value is obtained by changing its l’s to 0’s and the 0’s to l’s.
Examples
*One’s complement of 0100 is 1011
*One’s complement of 0000 is 1111
*One’s complement of 0110 is 1001 2’s complement of a binary number
*2’s complement of a binary value is obtained by
1.converting the value to its is complement, then
2.adding 1 to that complement
Example
2’s complement of 0110
step 1 : l’s complement of 0110 is 1001
step 2 : Adding 1 to 1001
1001 +
0001
1010
2’s complement of 0110 is 1010
Binary l's complement 2's Complement
0000 1111 oooo
0001 1110 1111
0010 1101 1110
0011 1100 1101
0100 1011 1100
0101 1010 1011
0110 1001 1010
0111 1000 1001
1000 0111 1000
1001 0110 0111
1010 0101 0110
1011 0100 0101
1100 0011 0100
1101 0010 0011
1110 0001 0010
1111 0000 0001
