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LOW POWER HIGH
    SPEED MULTIPLIERS

Submitted by:
          K.NAVYA        (09C81AO456)
          B.BHANU PRASAD (09C81AO416)
         B.SUVARNA KUMARI(09C81AO426)
          A.GANDHI        (09C81A0401)
INTRODUCTION
 Booth’s multiplication algorithm was invented by
  ANDREW BOOTH in 1951
 This algorithm is particularly useful for machines that
  can shift bits faster than adding them.
 Another improvement in the multiplier is by reducing the
  number of partial products generated.
 It operates even with signed numbers
BRAUN ARRAY MULTIPLIER
  braun edward louis first proposed the braun
  multiplier in 1963.
 it is a simple parallel multiplier that is commonly
  known as the carry array multiplier.
 This is restricted to performing multiplication of two
  unsigned numbers.
 It consists of an array of and gates and adders
  arranged in an iterative structure that does not require
  logic registers.
 This is also known as the non-additive multiplier
  since it does not add an additional operand to the
  result of the multiplication.
ARCHITECTURE OF BRAUN MULTIPLIER
 An n*n –bit braun multiplier requires n(n-1) adders
  and n2 and gates .
 The internal structure of the full adder used in the
  braun multiplier makes braun multipliers ideal for
  very large scale integration (vlsi) and application
  specific integrated circuit (asic) realization.
 each of the xiyj product bits is generated in
  parallel with the and gates.
 Each partial product can be added to the previous
  sum of partial products by using adders.
 The carry out signals are shifted one bit to the left
  and are then added to the sums of the first adder
  and the new partial product.
GENERAL MULTIPLICATION
PERFORMANCE :
 The braun multiplier performs well for
  unsigned operands that are less than 16 bits, in
  terms of speed, power and area.
 Besides, it has a simple and regular structure as
  compared to the other multiplier schemes.
 How ever, the number of components required
  in building the braun multiplier increases
  quadratically with the number of bits.
 This makes the braun multiplier inefficient and
  so it is rarely employed while handling large
  operands.
SPEED CONSIDERATION:
 The delay of the braun multiplier i is dependent on the
  delay of the full adder cell and also on the final adder
  in the last row.
 In the multiplier array, a full adder with balanced
  carry and sum delays is desirable because the sum and
  carry signals are both in the critical path.
 The speed and power of the full adder is very
  important for large arrays.
BOOTH’S MULTIPLIER
 A multiplier has two stages.
 In the first stage, the partial products are
  generated by the booth encoder and the
  partial product generator (ppg), and are
  summed by compressors.
 In the second stage, the two final products
  are added to form the final product
  through a final adder.
BLOCK DIAGRAM
TRUTH TABLE
BOOTH’S MULTIPLICATION
OPERATION OF BOOTH
MULTIPLIER
 The booth encoder was implemented using two xor
  gates and the selector using 3muxes and an inverter
  careful optimization of the partial-product generation
  can lead to some substantial delay and hardware
  reduction.
 [8] in the normal 8*8 multiplication 8 partial products
  need to be generated and accumulated.
 For accumulation seven adders to reduce power are
  required but in the case of booth
SIMULATION OF BRAUN MULTIPLIER
SIMULATION OF BOOTH MULTIPLIER
ADVANTAGES
 Booth multiplier operates with high speed
 It has low complexity
 Low power consumption
 It has less access time
APPLICATIONS:
 It is arithmetic operation for dsp
  applications.
 Such as ‘filtering ‘, and for fourier
  transforms.
 To achieve high execution speed, parallel
  array multipliers are widely used .
 These multipliers tend to consume most
  of power in dsp computions
COMPARISON:

ARRAY MULTIPLIER                BOOTH S MULTIPLIER

1.Total power consumption is    1.Total power consumption is
267mW.                          263mW.
2.Time period is 13.553 nsec.   2.Time period is 2.52 nsec.
3.It has more complexity.       3.It has less complexity.
SUMMARY AND
CONCLUSION
 the braun array multiplier and booth
 multiplier was implemented using vhdl
 and the results are verified for the braun
 and booth multipliers.
Low power high_speed
Low power high_speed

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Low power high_speed

  • 1. LOW POWER HIGH SPEED MULTIPLIERS Submitted by: K.NAVYA (09C81AO456) B.BHANU PRASAD (09C81AO416) B.SUVARNA KUMARI(09C81AO426) A.GANDHI (09C81A0401)
  • 2. INTRODUCTION  Booth’s multiplication algorithm was invented by ANDREW BOOTH in 1951  This algorithm is particularly useful for machines that can shift bits faster than adding them.  Another improvement in the multiplier is by reducing the number of partial products generated.  It operates even with signed numbers
  • 3.
  • 4. BRAUN ARRAY MULTIPLIER  braun edward louis first proposed the braun multiplier in 1963.  it is a simple parallel multiplier that is commonly known as the carry array multiplier.  This is restricted to performing multiplication of two unsigned numbers.  It consists of an array of and gates and adders arranged in an iterative structure that does not require logic registers.  This is also known as the non-additive multiplier since it does not add an additional operand to the result of the multiplication.
  • 6.  An n*n –bit braun multiplier requires n(n-1) adders and n2 and gates .  The internal structure of the full adder used in the braun multiplier makes braun multipliers ideal for very large scale integration (vlsi) and application specific integrated circuit (asic) realization.  each of the xiyj product bits is generated in parallel with the and gates.  Each partial product can be added to the previous sum of partial products by using adders.  The carry out signals are shifted one bit to the left and are then added to the sums of the first adder and the new partial product.
  • 8. PERFORMANCE :  The braun multiplier performs well for unsigned operands that are less than 16 bits, in terms of speed, power and area.  Besides, it has a simple and regular structure as compared to the other multiplier schemes.  How ever, the number of components required in building the braun multiplier increases quadratically with the number of bits.  This makes the braun multiplier inefficient and so it is rarely employed while handling large operands.
  • 9. SPEED CONSIDERATION:  The delay of the braun multiplier i is dependent on the delay of the full adder cell and also on the final adder in the last row.  In the multiplier array, a full adder with balanced carry and sum delays is desirable because the sum and carry signals are both in the critical path.  The speed and power of the full adder is very important for large arrays.
  • 10. BOOTH’S MULTIPLIER  A multiplier has two stages.  In the first stage, the partial products are generated by the booth encoder and the partial product generator (ppg), and are summed by compressors.  In the second stage, the two final products are added to form the final product through a final adder.
  • 14. OPERATION OF BOOTH MULTIPLIER  The booth encoder was implemented using two xor gates and the selector using 3muxes and an inverter careful optimization of the partial-product generation can lead to some substantial delay and hardware reduction.  [8] in the normal 8*8 multiplication 8 partial products need to be generated and accumulated.  For accumulation seven adders to reduce power are required but in the case of booth
  • 15. SIMULATION OF BRAUN MULTIPLIER
  • 16. SIMULATION OF BOOTH MULTIPLIER
  • 17. ADVANTAGES  Booth multiplier operates with high speed  It has low complexity  Low power consumption  It has less access time
  • 18. APPLICATIONS:  It is arithmetic operation for dsp applications.  Such as ‘filtering ‘, and for fourier transforms.  To achieve high execution speed, parallel array multipliers are widely used .  These multipliers tend to consume most of power in dsp computions
  • 19. COMPARISON: ARRAY MULTIPLIER BOOTH S MULTIPLIER 1.Total power consumption is 1.Total power consumption is 267mW. 263mW. 2.Time period is 13.553 nsec. 2.Time period is 2.52 nsec. 3.It has more complexity. 3.It has less complexity.
  • 20. SUMMARY AND CONCLUSION  the braun array multiplier and booth multiplier was implemented using vhdl and the results are verified for the braun and booth multipliers.