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

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First represent 57 in binary that is 00111001

Now represent - 57 in binary by taking 2's complement that is 1  1  0  0  0  1  1  1

Taking LSB as q0 and MSB as qn where n is the number of bits

Pairwith column always start with $q_{-1}$ which is having value = 0 always in all these types of question. and rest of the values in this column we have to copy as it is from multiplier column bit by bit . Follow this table to get the recoded value

Bit-pair    Recoding

0 0                0

0 1                1

1 0               -1

1 1                0

By taking multiplier - 57 from right to left

Multiplier                        pairwith                              Recoded

1(q0)                            0($q_{-1}$)                            - 1  (LSB)

1(q1)                            1(q0)                                    0

1(q2)                            1(q1)                                    0

0(q3)                            1(q2)                                    1

0(q4)                            0(q3)                                    0

0(q5)                            0(q4)                                    0

1(q6)                            0(q5)                                  - 1

1(q7)                            1(q6)                                    0   (MSB)

Recoded = (0  -1   0   0   1   0   0  -1)

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