1
votes

## 1 Answer

2
votes

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)

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)