Draw a carry save adder tree using

$3$

:

$2$

$$counters

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i

$.$

e

$.$

$.$

$$full adders

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$$are building blocks

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wallace tree

$)$

$$to accumulate partial products in the multiplication of two operands in the two complement format, where each operand is

$15$

$$bit long. Assume that radix

$-$

$4$

$$Booth recoding is used. How many levels are there in the tree?, what is the length of the final CPA

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in terms of the number of digit positions across which the carry needs to propagate?, Let the delay of each

$-$

$$level be triangle

$3$

:

$2.$

$$then what is the total delay required by the tree to reduce the summation of partial products down to two operand,

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excluding the delay of booth

$-$

recoding

$)$

$?$

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$$Now draw another tree based on the

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$4$

$,$

$2$

$)$

$$compressors$.$ What is the length of final carry

$-$

$$propagate adder? Let the delay of each level be triangle

$1$

:

$2.$

$$Then what is the total delay of the tree? Derive conditions relating triangle

$3$

:

$2$

$$and triangle

$4$

:

$2$

$$under which

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a

$)$

$$The wallace Tree is faster and

$($

b

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$$The

$4$

:

$2$

$$compressor tree is faster