Q 5. Comprehension of stored value: what are these numbers in 2\'s complement sy
ID: 3733636 • Letter: Q
Question
Q 5. Comprehension of stored value: what are these numbers in 2's complement system (in computer memory these number are stored, what are these?) 1000 0000 1011 1011 Q 6.Answer the followings Write at least three advantages of 2's complement system to represent signed numbers. While representing Floating point numbers, what is meant by Range and Accuracy? How these can be affected? Lets computer stored numbers in 8 bits in 2's complement format, what is the largest and smallest number that can be stored? If we add 1 to the largest number what would happen? bvgif we subtract 1 from smallest number what would happen? a) b) c) d) Why exponent is stored as biased exponent in floating point representation? Activate WExplanation / Answer
SOLUTIONS:-
(5): 2's complement of 00000000 = 1 1 1 1 1 1 1 1 ( convert every 0's into 1's = 1's complement)
+ 1 ----------------------- 100000000 (2's Complement) -----------------------
Number = (- 256)
2's complement of 10000000 = 1 1 1 1 1 1 1 ( convert every 0's into 1's = 1's complement)
+ 1 ----------------------- 1 0 0 0 0 0 0 0 (2's Complement) -----------------------
Number = (- 128)
2's complement of 11111111 = 0 0 0 0 0 0 0 0 ( convert every 0's into 1's = 1's complement)
+ 1 ----------------------- 0 0 0 0 0 0 0 1 (2's Complement) -----------------------
Number = (- 1)
2's complement of 01111111 = 1 0 0 0 0 0 0 0 ( convert every 0's into 1's = 1's complement)
+ 1 ----------------------- 1 0 0 0 0 0 0 1 (2's Complement) -----------------------
Number = (- 127)
2's complement of 10111011 = 1 0 0 0 1 0 0 ( convert every 0's into 1's = 1's complement)
+ 1 ----------------------- 1 0 0 0 1 0 1 (2's Complement) -----------------------
Number = (- 59)
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(6)(a):- Advantages of 2's complement are given below:-
(1) It contains only one value for 0
(2) carry values are not required
(3) Simple and Easy manipulation in Harware Circuits.
(6)(b):- In floating point representation, Number of Significant bits controls Accuracy and Exponent decides the limit of the Range.
In n bit 2's complement notation The Range can be calcluated = - (2(n-1)) to + (2(n-1) -1)
(6)(c):- 8 bits Smallest Number in 2's complement format = (- 128)
8 bits Largest Number in 2's complement format = (127) {By Applying - (2(n-1)) to + (2(n-1) -1) }
(6)(d):- We can get the value of stored exponent by adding the bias to its actual exponent.
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