Explain Booth multiplication algorithm with hardware implementation diagram. Multiply (-4) x (-3) using Booth multiplication algorithm.

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Booth algorithm gives a procedure for multiplying binary integers in signed 2’s complement notation

Hardware Implementation:

 

- Hamro CSIT

  • Here, sign bit are not separated
  • Registers A, B and Q are renamed to AC, BR and QR
  • Extra flip-flop Qn+1 is appended to QR which stores almost lost right shifted bit of the multiplier.
  • Pair QnQn+1 inspect double bits of the multiplier

Problem:

Solution:

Multiplication (M) = (-4)10 = 1100

Multiplication (-M) = (+4)10 = 0100

Q = (-3)10 = 1101

Now,

Steps AC Q Qn-1 Operation
0000 1101 0 Initial
1st 0100 1100 0 AC = AC – M
0010 0110 1 Right Shift
2nd 1110 0110 1 AC = Ac + M
1111 0011 0 Right Shift
3rd 0011 0011 0 AC = AC – M
0001 1001 1 Right Shift
4th 0000 1100 1 Right Shift

Hence,

Result = AC and Q

i.e. 0000 1100

Therefore, Result = (-4)10 x (-3)10 = (12)10

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