When multiplicand Y is multiplied by multiplier X = xn - 1xn-2 ....x0 using…
2006
When multiplicand Y is multiplied by multiplier X = xn - 1xn-2 ....x0 using bit-pair recoding in Booth's algorithm, partial products are generated according to the following table.
The partial products for rows 5 and 8 are
- A.
2Y and Y
- B.
-2Y and 2Y
- C.
-2Y and 0
- D.
0 and Y
Attempted by 9 students.
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Correct answer: C
Key idea: use Booth bit-pair recoding to map each triplet (xi+1 xi xi-1) to the corresponding partial product.
000 -> 0
001 -> +Y
010 -> +Y
011 -> +2Y
100 -> -2Y
101 -> -Y
110 -> -Y
111 -> 0
Apply the mapping to the specified rows:
Row 5 has triplet 100 -> -2Y.
Row 8 has triplet 111 -> 0.
Therefore the partial products for those rows are -2Y and 0.