Q: GATE(CS) 2013
Q 1. The smallest integer that can be represented by a bit number in 2 complement form is
(A) -256
(B) -128
(C) -127
(D) 0
Before seeing the answer follow: Signed representation by 2’s Complement
Solution:
With n bits, the range of numbers that can be represented in 2´s complement form is
So the smallest number is
So, option (B) is the correct answer.
Q: UGC NET: 2014, Q. 17
7) Which of the following is the most efficient to perform arithmetic operations on the numbers?
a) Sign-magnitude
b) 1’s complement
c) 2’s complement
d) 9’s complement
Solution:
Option (c) is the correct answer.
Explanation:
In sign-magnitude, there are two representations for zero (0)
# In 1’s complement also there are two representations for zero (0).
# In 9’s complement also there are two representations for zero (0).
# In 2’s complement, there is only one representation for zero (0)
Advantages of 2´s complement representation over the signed magnitude and its complement
1. 2´s complement has only one value for zero, i.e. 2´s complement has the same representation of +0 and -0, unlike other representations.
2. 2´s complement arithmetic is faster than 1´s complement arithmetic as there is no need for correction of end-around carry (EAC).
In the 2’s complement system is that only one arithmetic operation is required; the 1’s complement requires two operations, (we have to add an extra carry bit i.e., 1 to the result of addition or subtraction to get the correct answer).
∴ In the case of performing the arithmetic operations, 2’s complement is the most efficient method.
So, answer: Option (c) 2’s complement.
Q. 2. GATE CS 2010
P is a 16 bit signed integer. The 2´s complement representation of P is . The 2´s complement representation of 8 * P is
Before seeing the answer please follow chapter:
Signed representation by 2’s Complement
Decimal to Hexadecimal and Hexadecimal to Decimal
Solution:
∴ Option (A) is correct.
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