Ace exam

Question

I am getting aswer as 70ns with 1 exor gate + 1 or gate + 2 and gate... but given answer is 60ns, where they have mention as 1 exor gate + 1 or gate + 1 and gate.. my doubt is why we are considering only 1 AND gate.. when there is 2 AND gate require to produce cout..  

https://gateoverflow.in/8250/gate2015-2_48, here is one similar question, at the start its also considering delay due to 1 AND gate only.. 

Comments

@mcjoshi

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@Chauhan answered.

Answer 1

This is how an full adder is implemented using XOR gate, AND and OR gates.

$C_{out} = (A\oplus B)C + AB$

We compute $A \oplus B$ and $AB$ parallely here, So time taken to compute $A \oplus B$ and $AB$ is equal to the maximum of time taken to compute these two individually = $max(A \oplus B,AB) = 30ns$

Now, We find $ (A\oplus B)C $ next which takes additional $10ns$ due to AND gate and next we OR $(A\oplus B)C$ and $AB$, which takes additional $20ns$ time.

So, total time taken to find out Carry $= 30 + 10 +20 = 60ns$

Comments

@Anirudh thks

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Time for the sum+ carry will also remains 60,right? By 60 the second exor will also produce sum and parallely carry is also produced.Am i correct?

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yes, both sum and carry will be out at '60'