Using Booth's Algorithm for multiplication, the multiplier -57 will be recoded…

Solution: Apply Booth's algorithm to -57 using 8-bit representation.

Step 1: 8-bit two's complement representation of -57: 11000111 (bits y7..y0 = 1 1 0 0 0 1 1 1).

Step 2: Set y_{-1} = 0 (implicit zero below LSB).

• i = 0: (y0, y_{-1}) = (1, 0) -> digit -1

• i = 1: (y1, y0) = (1, 1) -> digit 0

• i = 2: (y2, y1) = (1, 1) -> digit 0

• i = 3: (y3, y2) = (0, 1) -> digit +1

• i = 4: (y4, y3) = (0, 0) -> digit 0

• i = 5: (y5, y4) = (0, 0) -> digit 0

• i = 6: (y6, y5) = (1, 0) -> digit -1

• i = 7: (y7, y6) = (1, 1) -> digit 0

Final Booth recoding (from MSB to LSB): 0 -1 0 0 1 0 0 -1