The 3 input AND gate

I’d come across this tricky question at one of the interviews. Here’s it.

Q : In how many ways can you realize a 3-input AND gate using 2-input AND gates?

A : The answer is obviously 2 ways as shown below.

Q : Now, you are given a “Black Box” of 3 input AND gate and the method of realization used internally is unknown. How can you determine the internal composition used?

A : The only instinctive hint is the delay caused for change in input to reflect at the output. Here’s how:

Step 1: Set all inputs to ‘1’ so that output is ‘1’. Now, change input A to ‘0’.

Step 2: Again set all inputs to ‘1’ so that output is ‘1’. Now, change input B to ‘0’.

Step 3: Again set all inputs to ‘1’ so that output is ‘1’. Now, change input C to ‘0’.

Observe the output waveforms of the above 3 cases. If the timing at which the output state changes from ‘1’ to ‘0’ in all the waveforms is same, then the second structure is used; because, second structure needs 2 gate delays for change at output in all above cases. If in one of the waveforms, the change in state from ‘1’ to ‘0’ at output occurs earlier, compared to waveforms of other 2 cases, then, first structure is used.

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