Page 49 - ComputerScience_Class_11

b. 1’s complement of 110111.10 is 001000.01 +1 +1
2’s complement of 001000.01 is 001000.10 1 0 0 0 . 0 1
Adding 1000.01 and 001000.10, we get + 0 0 1 0 0 0 . 1 0

0 1 0 0 0 0 . 1 1
1’s complement of 010000.11 is 101111.00
(-101111.01) 2 2’s complement of 101111.00 is 101111.01
16. Perform the octal addition (1567.2) + (433.4) 8
8
Ans. +1 +1 +1
1 5 6 7 . 2
+ 4 3 3 . 4
2 2 2 2 . 6
(2222.6) 8
17. Perform octal subtraction (3214.6) - (777.7) using:
8
8
a. Borrow method
b. 7’s complement method
c. 8’s complement method
Ans. a.
+8 +8 +8 +8
3 2 2 1 1 0 4 3 . 6
7 7 7 . 7
2 2 1 4 . 7

(2214.7) 8
b. 7’s complement of 0777.7 is 7000.0 +1
Adding 3214.6 and 7000.0, we get 3 2 1 4 . 6
+ 7 0 0 0 . 0
1 2 2 1 4 . 6
1
(2214.7) 2 2 1 4 . 7
8
c. 7’s complement of 0777.7 is 7000.0 +1
8’s complement of 7000.0 is 7000.1 3 2 1 4 . 6
Adding 3214.6 and 7000.1, we get + 7 0 0 0 . 1
Discarding MSB 1, we get 1 2 2 1 4 . 7
(2214.7) 8
18. Perform octal subtraction (361) - (2143) using:
8
8
a. 7’s complement method
b. 8’s complement method
Ans. a. 7’s complement of 2143 is 5634 +1 +1
Adding 361 and 5634, we get 3 6 1
7’s complement of 6215 is 1562 + 5 6 3 4
(-1562) 8 6 2 1 5
b. 7’s complement of 2143 is 5634
8’s complement of 5634 is 5635 +1 +1
Adding 361 and 5635, we get 3 6 1
7’s complement of 6216 is 1561 + 5 6 3 5
8’s complement of 1561 is 1562 6 2 1 6
(-1562) 8

System of Numeration 47