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I'm trying to answer a question on propagation delay. The question is:

Assuming the propagation delays for different circuits are as follow:

  • 4 ns for XOR gate,
  • 3 ns for OR gate,
  • 5 ns for NAND gate and
  • 12 ns for a 4-by-1 multiplexer,

calculate the propagation delay for a change at input A to reach the output F, when all other inputs are constant.

The circuit is below The Circuit

I have calculated the propagation delay to be 14ns. Is this correct?

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  • \$\begingroup\$ Please show your work and assumptions. \$\endgroup\$ – placeholder May 28 '16 at 17:42
  • \$\begingroup\$ 4ns for xor gate, 5ns for 1st nand gate, total 9ns. 3ns for or gate. so 9ns for the input to get to the 2nd nand gate plus 5ns for the 2nd nand gate so totally its 9ns+5ns = 14ns. \$\endgroup\$ – user3472448 May 28 '16 at 17:47
  • \$\begingroup\$ Write little numbers above each gate. Follow the signal. Add up the numbers. NOTE: this assumes gates are close together physically. \$\endgroup\$ – mkeith May 28 '16 at 17:47
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    \$\begingroup\$ Let me be a little clearer. This is not a discussion site but a Q & A site, we are looking for problems that can be generalized and thus used by other people in the future. That is why we don't answer explicit homework problems. In this case you are asking for confirmation of you thoughts, the problem with that is that this will only answer this problem. If you repose it with an analysis and stated assumptions then someone else in the future can then generalize this to answer a different problem. \$\endgroup\$ – placeholder May 28 '16 at 17:50
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    \$\begingroup\$ It may have started out poor, but the current worked and illustrated form of this question is an example of the way in which a homework problem can belong on the site. Placeholder seems to misunderstand the rules about generalization - specific cases are fine as long as they are complete and self-contained - which makes them useful examples. \$\endgroup\$ – Chris Stratton May 28 '16 at 18:06
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IMHO there are two anwsers:

  1. "Infinite" - when B=0 & D=1
  2. 14ns (in this idealized question).

The propagation delay of a signal is indeed the sum of all the delays in the longest path. In the example, if A would also be an input to the 'OR' port, there might be two changes in the output, but the stable output is only reached after the longest path has settled.

The "infinite" case is not usually considered but I consider it for completeness.

In practice, propagation delays depend on the transition type (up/down), temperature, voltage and manufacturing process (those are the ones that are considered when designing integrated circuits).

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