Computer Arithmetic

Why are carry-save adders used to sum the many partial products in a multiplier?

  1. AA carry-save adder reduces the partial products to one from the start
  2. BA carry-save adder performs multiplication without any addition
  3. CIt reduces three numbers to two without carry propagation
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Answer: C. It reduces three numbers to two without carry propagation

Adding partial products one at a time with ordinary adders means waiting each time for carries to ripple from low to high bits. A carry-save adder is just full adders placed independently per bit, reducing three numbers to two (the per-bit sums and the per-bit carries) without waiting for carry propagation, so its delay is a constant one full-adder level. Stages of these reduce the partial products to two, which are added once at the end by a carry-lookahead adder or similar. It cannot reduce them to one in a single step.

  • A. It reduces three to two, not to one.
  • B. It is used for the very additions that sum the partial products.
  • C. Correct. It reduces three to two without carry propagation, with constant delay.
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More Computer Arithmetic questions

  1. Which describes a Wallace tree used in fast multipliers?
  2. What is the main effect of using radix-4 Booth's algorithm (Booth encoding) in a multiplier?
  3. When two unsigned 8-bit numbers are multiplied, how many bits are needed to represent the result without overflow?
  4. Which expression multiplies an integer x by 10 using shifts and additions instead of a multiply instruction?
  5. Why do typical integer dividers (restoring or non-restoring, producing one quotient bit at a time) tend to be slower than multipliers?