14 Multiplication Methods Flashcards

1
Q

Example of implementation of a multiplier

A
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2
Q

Binary multiplications?

A
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3
Q

Circuit realization of Binary multiplication?

A
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4
Q

The number of AND gates, stage holders and bits required for a multiplication?

A
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5
Q

Thus, for a 4 x 4 multiplier we will need: 16 AND gates and 3 stages of adders to produce 8 bits.

A
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6
Q

How can problems occur when multiplying negative numbers?

A
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7
Q

Process to compute the correct multiplication of negative number using the unsigned multiplier plus additional hardware.

A
  • If a negative number is present, then take its two’s complement to obtain its equivalent magnitude (positive representation).
  • Multiply input values with their positive representation.
  • Apply the correct sign to the final product
  • If the product should be negative, then take the two’s complement in the final result.
  • This creates a number that is in two’s complement format
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8
Q

The correct method for multiplying 7 and -7

A
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9
Q

What is Booth’s algorithm

A

Booth’s algorithm attempts to reduce the complexity of a multiplication by replacing multiple adders with a shift register and an adder/subtractor.

This algorithm was developed to speed up the multiplication of two signed numbers.

No need to compute the sign of the final product performed by the traditional multiplication procedure

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10
Q

Booths algorithm Definitions?

A

Let M be the multiplicand.

Let Q be the multiplier.

Consider a 1-bit register Q-1 initialised to 0.

Consider a register A initialised to 0.

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11
Q

Booth algorithm Condictions?

A
  • If Q0 and Q-1 are the same (00 or 11), then perform arithmetic right shift by 1 bit.
  • If Q0 and Q-1 are 10, then perform A = A – M and arithmetic right shift.
  • If Q0 and Q-1 are 01, then perform A = A + M and arithmetic right shift.
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12
Q

The Wallace Tree diagram?

A
  • As multiplications get larger sequential addition processes becomes inefficient.
  • Wallace tree algorithm suggest to add terms (bits) as soon as possible.
  • The idea of Wallace tree algorithm is “divide & conquer” (divide partial products).
  • Fast addition is possible across all the bit slices.
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13
Q

The stages of the Wallace tree diagram.

A

Stage 1: partial products

Stage 2: addition of partial products

Stage 3: final addition

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14
Q

Advantages and disadvantages of wallace tree?

A

This is process is fast because all the adders are done in parallel!

This is a fast multiplication algorithm but it requires large number of logic gates.

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15
Q
A
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