Simplification of a digital circuit

momentum · Sep 16, 2020

I am trying to solve this problem

I have solved this myself in two different ways, but i am getting different results.

Solution # 1

Handwritten Boolean algebra simplification: (AC bar + AC bar) = A bar(A bar + B bar) + A bar(A bar + B bar), simplified step by step through AB + AB + A, down to A bar(1 + 1 + B bar) + B, ending at = A bar + B.

Solution # 2

Handwritten Boolean algebra derivation: AB + A'B = C (given), then A + B' + A'B = C, then A' + AB + B' = C, then A'(1 + B) + B' = C, then A' + B' = C.

Now to find :

Handwritten Boolean algebra derivation: A'C + A'C = A' + C' + A'C = A' + A'C + C = A'(1 + C) + C = A' + C, then with an arrow labelled 'applying C' = A' + A' + B = A' + B.

Please see output is different in solution#1 and solution#2.

Which solution is correct ? Is there anything I am missing.

DaveE · Sep 16, 2020

recheck your work there is a simple error.

momentum · Sep 16, 2020

DaveE said:

recheck your work there is a simple error.

Could you please be specific ? where is the error ? I am unable to find it.

DaveE · Sep 16, 2020

line 3 in the last box.

Often a good way to check when things don't seem right is to just redo the problem, for small problems, anyway.

DaveE · Sep 16, 2020

You might also notice that both of the original equations can be simplified (they have the same form) before you do any substitutions. That isn't necessary, just another approach.

If you've learned about Karnaugh Maps this would be a good place to use them too. Again, not necessary, just another option.

momentum · Sep 17, 2020

Thanks. I spotted error. This helped a lot.

What is a good way to test if my solution is correct or not for such questions ? ( in general )

For example , in this problem , Is there any way to test or verify if my arrived solution is correct or not ? ( may be by using some data points or some process )

Simplification of a digital circuit

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