###### GATE 2007

October 14, 2023###### GATE 2007

October 14, 2023# GATE 2017 [Set-1]

Question 9 |

When two 8-bit 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 ripple-carry 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

⇾ Overflow can be detected by checking carry into the sign bits (C

⇾ Overflow occurs iff A

These conditions are equivalent to

Consider

Here A

This happens only if C

Carry out C

Similarly, in case of

C

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}= 0This happens only if C

_{in}= 0Carry out C

_{out}=1 whenSimilarly, 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

⇾ Overflow can be detected by checking carry into the sign bits (C

⇾ Overflow occurs iff A

These conditions are equivalent to

Consider

Here A

This happens only if C

Carry out C

Similarly, in case of

C

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}= 0This happens only if C

_{in}= 0Carry out C

_{out}=1 whenSimilarly, in case of

C

_{in}=1 and C_{out}will be 0. Subscribe

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