- #1

jaus tail

- 615

- 48

- Homework Statement
- Find the longest path in the circuit

- Relevant Equations
- Find out which paths won't be ever evaluated or make any difference, remove those paths, and then add individual delays

First for logic-1 at output: So I get that for Logic 1, the OR-2 Gate must have one input has logic-1.

Case1: Upper OR-Input is 1 of second OR Gate. So the longest path is Inv-1, Or-1, Or-2. Delay is 9ns.

Case2: For lower input to be 1, the 'And-2' output has to be 1, and for that Or-1 output has to be 1. So same as Case1. Delay = 9ns

For logic-0 at output. Both inputs for Or-2 have to be zero. For upper input of Or-2 to be zero, A=0, B =1. Delay is 5ns (B-path. 1 + 4) for this to reach Or-2

And for lower input of Or-2 to be zero, and 'And-2' output has to be zero. But this will be zero as Or-2 output is zero. So this will take 1 + 4 + 3 ns

Max time = 1 + 4 + 3 + 4 = 12 ns

Longest path:

However, the solution says that the longest path is Inv-1, Or-1, Or-2. But the last gate is an Or and not an And gate. Unless it gets both its inputs as 0,0 we can't be sure that output will remain at 0.

I agree that once the upper input to the Or-2 gate is 0, even the lower one will be 0 only as the upper input is coming to lower one via an 'And' gate.

But till then the lower input is floating. What if the output of this circuit was 1 earlier and the And'2 had 1 as output and now the output is becoming 0. In that case it will wait for the green path to execute before giving the correct output.