Consider a pipeline unit for fixed-point multiplication of 8-bit integers.…
2025
Consider a pipeline unit for fixed-point multiplication of 8-bit integers. Arrange the following stages in a correct sequence.
Stage A: Consists of two CSAs and it merges four numbers from previous stage.
Stage B: is a CPA, which adds up the two numbers.
Stage C: is made up to two level of four CSAs.
Stage D: Generates eight partial products.
Choose the correct answer from the options given below:
Answer: B. D, C, A, B — Correct sequence (first to last): generate partial products → reduce with CSA tree → merge CSA outputs → final carry-propagate addition. Generate eight…
- A.
C, A, B, D
- B.
D, C, A, B
- C.
B, D, C, A
- D.
A, C, D, B
Attempted by 42 students.
Show answer & explanation
Correct answer: B
Correct sequence (first to last): generate partial products → reduce with CSA tree → merge CSA outputs → final carry-propagate addition.
Generate eight partial products: Produce the bitwise partial products from the multiplicand and multiplier. This is the starting set of operands that must be summed.
Reduce using up to two levels of four carry-save adders: Use a CSA tree to compress the eight partial products into fewer intermediate sums and carries without performing full carry propagation.
Merge four numbers using two carry-save adders: Further compress the remaining four intermediate operands into two numbers (a sum and a carry) ready for the final addition.
Final carry-propagate addition: Use a CPA to add the final two operands (sum and carry) with full carry propagation to produce the complete product.
Reasoning: Carry-save adders are used to reduce multiple operands without inter-stage carry propagation, so partial products must be generated first and then progressively reduced by CSA stages. Only after reduction to two operands should a carry-propagate adder be used to obtain the final result.
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