GATE 2007
October 14, 2023GATE 2007
October 14, 2023GATE 2017 [Set1]
Question 9

When two 8bit numbers A_{7}…A_{0} and B_{7}…B_{0} in 2’s complement representation (with A_{0} and B_{0} as the least significant bits) are added using a ripplecarry adder, the sum bits obtained are S_{7}…S_{0} and the carry bits are C_{7}…C_{0}. An overflow is said to have occurred if
the carry bit C_{7} is 1


all the carry bits (C_{7},…,C_{0}) are 1


Question 9 Explanation:
⇾ Overflow may occur when numbers of same sign are added
i.e., A_{7} = B_{7}
⇾ Overflow can be detected by checking carry into the sign bits (C_{in}) and carry out of the sign bits (C_{out}).
⇾ Overflow occurs iff A_{7} = B_{7} and C_{in} ≠ C_{out}
These conditions are equivalent to
Consider
Here A_{7} = B_{7} = 1 and S_{7} = 0
This happens only if C_{in} = 0
Carry out C_{out}=1 when
Similarly, in case of
C_{in}=1 and C_{out} will be 0.
i.e., A_{7} = B_{7}
⇾ Overflow can be detected by checking carry into the sign bits (C_{in}) and carry out of the sign bits (C_{out}).
⇾ Overflow occurs iff A_{7} = B_{7} and C_{in} ≠ C_{out}
These conditions are equivalent to
Consider
Here A_{7} = B_{7} = 1 and S_{7} = 0
This happens only if C_{in} = 0
Carry out C_{out}=1 when
Similarly, in case of
C_{in}=1 and C_{out} will be 0.
Correct Answer: C
Question 9 Explanation:
⇾ Overflow may occur when numbers of same sign are added
i.e., A_{7} = B_{7}
⇾ Overflow can be detected by checking carry into the sign bits (C_{in}) and carry out of the sign bits (C_{out}).
⇾ Overflow occurs iff A_{7} = B_{7} and C_{in} ≠ C_{out}
These conditions are equivalent to
Consider
Here A_{7} = B_{7} = 1 and S_{7} = 0
This happens only if C_{in} = 0
Carry out C_{out}=1 when
Similarly, in case of
C_{in}=1 and C_{out} will be 0.
i.e., A_{7} = B_{7}
⇾ Overflow can be detected by checking carry into the sign bits (C_{in}) and carry out of the sign bits (C_{out}).
⇾ Overflow occurs iff A_{7} = B_{7} and C_{in} ≠ C_{out}
These conditions are equivalent to
Consider
Here A_{7} = B_{7} = 1 and S_{7} = 0
This happens only if C_{in} = 0
Carry out C_{out}=1 when
Similarly, in case of
C_{in}=1 and C_{out} will be 0.
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