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Consider an eight-bit ripple-carry adder for computing the sum of A and B, where A and B are integers represented in 's complement form. If the decimal value of A is one, the decimal value of B that leads to the longest latency for the sum to stabilize is ___________
- a)-1
- b)2
- c)1
- d)-2
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Consider an eight-bit ripple-carry adder for computing the sum of A an...
Here "longest latency for the sum to stabilize" means maximum delay that ripple carry adder would take to add A and B, we are given value of A and need to find the value of B.
The Delay in Ripple Carry Adder is as follows
- For sum there are 2 XOR gates.
- For carry there is 1 XOR,1 AND and 1 OR gate.
i.e total 3 gate delays in case of carry and 2 gate delays in sum.
If we do 2's complement of 1 in 8 bit we get "00000001".
same we do for each option
-1 : "11111111"
2 : "00000010"
1 : "00000001"
-2 : "11111110"
So in case of -1 the carry bit will change and thus it will take 1 extra gate delay, hence we could see that the maximum delay we could get when input at B will be -1, i.e. add “00000001” with “11111111” and would get Maximum delay.
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Consider an eight-bit ripple-carry adder for computing the sum of A an...
Explanation:
In an eight-bit ripple-carry adder, the sum of two eight-bit numbers (A and B) is calculated by adding each corresponding bit and propagating the carry from one bit to the next. The sum will stabilize when there are no more carries to propagate.
To determine the decimal value of B that leads to the longest latency for the sum to stabilize, we need to consider the worst-case scenario for carry propagation.
Understanding s complement form:
In s complement form, the most significant bit (MSB) represents the sign of the number. For positive numbers, the MSB is 0, and for negative numbers, the MSB is 1. The remaining bits represent the magnitude of the number.
Case 1: A = 1 (decimal)
Since A is positive, the MSB of A is 0. To maximize the latency for the sum to stabilize, we need to find the largest negative number for B.
Case 1: B = -1 (decimal)
In s complement form, -1 is represented as all 1s. Therefore, B will be represented as 11111111 (eight bits).
Carry Propagation:
When adding A = 1 and B = -1, the LSB (bit 0) will have a carry of 1, which needs to be propagated to the next bit. This carry will propagate through all the bits, resulting in a delay in the stabilization of the sum.
Latency:
The latency for the sum to stabilize is directly proportional to the number of bits through which the carry propagates. In an eight-bit ripple-carry adder, the carry must propagate through all the eight bits. Therefore, the latency for the sum to stabilize will be maximum when A = 1 and B = -1.
Conclusion:
The decimal value of B that leads to the longest latency for the sum to stabilize when A = 1 is -1.
In an eight-bit ripple-carry adder, the sum of two eight-bit numbers (A and B) is calculated by adding each corresponding bit and propagating the carry from one bit to the next. The sum will stabilize when there are no more carries to propagate.
To determine the decimal value of B that leads to the longest latency for the sum to stabilize, we need to consider the worst-case scenario for carry propagation.
Understanding s complement form:
In s complement form, the most significant bit (MSB) represents the sign of the number. For positive numbers, the MSB is 0, and for negative numbers, the MSB is 1. The remaining bits represent the magnitude of the number.
Case 1: A = 1 (decimal)
Since A is positive, the MSB of A is 0. To maximize the latency for the sum to stabilize, we need to find the largest negative number for B.
Case 1: B = -1 (decimal)
In s complement form, -1 is represented as all 1s. Therefore, B will be represented as 11111111 (eight bits).
Carry Propagation:
When adding A = 1 and B = -1, the LSB (bit 0) will have a carry of 1, which needs to be propagated to the next bit. This carry will propagate through all the bits, resulting in a delay in the stabilization of the sum.
Latency:
The latency for the sum to stabilize is directly proportional to the number of bits through which the carry propagates. In an eight-bit ripple-carry adder, the carry must propagate through all the eight bits. Therefore, the latency for the sum to stabilize will be maximum when A = 1 and B = -1.
Conclusion:
The decimal value of B that leads to the longest latency for the sum to stabilize when A = 1 is -1.
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Consider an eight-bit ripple-carry adder for computing the sum of A and B, where A and B are integers represented in 's complement form. If the decimal value of A is one, the decimal value of B that leads to the longest latency for the sum to stabilize is ___________a)-1b)2c)1d)-2Correct answer is option 'A'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Consider an eight-bit ripple-carry adder for computing the sum of A and B, where A and B are integers represented in 's complement form. If the decimal value of A is one, the decimal value of B that leads to the longest latency for the sum to stabilize is ___________a)-1b)2c)1d)-2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider an eight-bit ripple-carry adder for computing the sum of A and B, where A and B are integers represented in 's complement form. If the decimal value of A is one, the decimal value of B that leads to the longest latency for the sum to stabilize is ___________a)-1b)2c)1d)-2Correct answer is option 'A'. Can you explain this answer?.
Consider an eight-bit ripple-carry adder for computing the sum of A and B, where A and B are integers represented in 's complement form. If the decimal value of A is one, the decimal value of B that leads to the longest latency for the sum to stabilize is ___________a)-1b)2c)1d)-2Correct answer is option 'A'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Consider an eight-bit ripple-carry adder for computing the sum of A and B, where A and B are integers represented in 's complement form. If the decimal value of A is one, the decimal value of B that leads to the longest latency for the sum to stabilize is ___________a)-1b)2c)1d)-2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider an eight-bit ripple-carry adder for computing the sum of A and B, where A and B are integers represented in 's complement form. If the decimal value of A is one, the decimal value of B that leads to the longest latency for the sum to stabilize is ___________a)-1b)2c)1d)-2Correct answer is option 'A'. Can you explain this answer?.
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