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$1)$3-bit ripple adder, which adds two 3-bit numbers, is designed using AND, OR, NOT, NAND, NOR gates only. Assuming that all the inputs are available in both complemented and uncomplemented forms and the delay of each gate is one time unit, what is the overall propagation delay of the adder

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$2)$3-bit carry look ahead adder, which adds two 3-bit numbers, is designed using AND, OR, NOT, NAND, NOR gates only. Assuming that all the inputs are available in both complemented and uncomplemented forms and the delay of each gate is one time unit, what is the overall propagation delay of the adder?

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1) In Ripple Carry Adder, only carry is propagated. So, 3 Full Adder is sufficient to add two 3-bit numbers.

Now,  among these Gates EXOR has maximum propagation delay.

And 1 EXOR can be made of 2 time unit in AND-OR gates. 

If LSB is Half adder,

So, propagation delay will be 2n-1=5 time unit

(Here Carry is propagating with sum)

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2) I tried to put Carry Look Ahead  adder in a diagram.

Here All adder are parallel and carry is propagated

Acc to wiki

  • calculation of  $P_{i}$and  $G_{i}$ is done at time 1,
  • calculation of $C_{i}$ is done at time 3,
  • calculation of the $PG$is done at time 2,
  • calculation of the $GG$is done at time 3, 

https://en.wikipedia.org/wiki/Carry-lookahead_adder

Here for 3-bit addition $GG$ will be  2 time  unit and $PG$ will be 2 time unit and $C_{0}$ will be 1 time unit

So, $C_{3}=G_{2}+G_{1}.P_{2}+G_{0}.P_{1}.P_{2}+C_{0}.P_{0}.P_{1}.P_{2}$

here $2+2\times 1=4$ time unit

Ans-4

(In Carry Look Ahead Adder  carry and sum propagating differently . In Ripple Carry and in CLA both case we concentrate only on Carry, not on Sum , as carry propagated upto last both the case )

http://faculty.kfupm.edu.sa/COE/abouh/Lesson3_2.pdf

http://faculty.kfupm.edu.sa/COE/abouh/Lesson3_3.pdf

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For ripple carry adder answer will be 8 time unit and for carry look ahead adder the answer will be 6 time unit.

In ripple carry adder(n bit adder):- Assuming fan-in atmost 2 and LSB's are computed using full adder.

Tpropagation =(n-1)* T.carry generation time by one full adder+ max(T.carry, T.sum)

   = 2*2  (2 because C=AB+BC+AC can be implemented in 2 levels of AND, OR gate) + max(4, 2)

T.sum=4 because A⊕B⊕C can be implemented using 4 levels of AND, OR gate only if variables are given in both complemented and uncomplemented form.

Tpropagation for ripple carry adder = 8

In carry look ahead adder(n bit adder):-

Carry look ahead adder works in three phases

The first level will take 2 time unit to generate all Pi, Gi terms using AND-OR gate in 2 levels only if variables are given in both complemented and uncomplemented form. similarly 2nd level will also take further 2 time unit for generating the all carry terms and after that to produce the sum terms it will take further 2 time unit. so total propagation delay is 6 time unit.

for more-https://www.gatevidyalay.com/delay-in-ripple-carry-adder/

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