Question

How to simplify Boolean expression from digital electronics?

Answer 1

I am having trouble finding a good method for simplifying a long Boolean expression representing a digital electronics circuit. There are 4 inputs: P, V, S, and T, and the circuit is represented by 8 unique terms that are various versions of those 4 terms connected by ANDs, e.g. P'VST, PV'ST, etc.

I have the final solution, and I can work backward a couple of steps, but otherwise, I am not seeing how to start from the original 8 terms and simplify to the final solution.

Answer 2

Here's the expression:
PVS'T + PVS'T' + PV'ST' + PV'S'T + PVST' + PV'ST + PVST + P'VST

It should simplify to P(V + S + T) + P'VST

I think the next-to-last step is PV + PS + PT + P'VST, but I have tried a lot of intermediate steps and have yet to be able to connect the start and finish.

Any help is appreciated... thanks!

Answer 3

what does ' mean and what does + mean

Answer 4

I used the ' to mean "NOT" so, P' means NOT P
+ is interpreted as OR
and terms that appear to be products are ANDs

So P'V is read as "(not P) and ( V )"

I didn't know how to type it any better or using alternate symbols that would be more clear .

Answer 5

and PV + P'V would be (P and V) or (not P and V) which would simplify to V(P + P') ("V and (P or not P) which simplifies to V( 1 ), or just V.

Answer 6

K table?

Answer 7

What do you mean by K table?

Answer 8

PVS'T + PVS'T' + PV'ST' + PV'S'T + PVST' + PV'ST + PVST + P'VST

P[VS'T + VS'T' + V'ST' + V'S'T + VST' + V'ST + VST] + P'VST

P[V'S'T + V'ST' + V'ST + VS'T' + VS'T + VST' + VST] + P'VST

P[V'S'T + V'S(T' + T) + VS'(T' + T) + VS(T' + T)] + P'VST

P[V'S'T + V'S + VS' + VS] + P'VST

P[V'(S'T + S) + V(S' + S)] + P'VST

Answer 9

we use this property : \(X + X'Y = X+Y\)

Answer 10

P[V'(T + S) + V] + P'VST

P[T + S + V ] + P'VST

Answer 11

@ganeshie8 - thanks so much for your help. Sorry I didn't respond earlier, but I did look at the simplification of the Boolean expression. I still find it straightforward to read the simplification but very hard to see opportunities to use the Boolean properties/theorems to combine and eliminate terms. Anyway, thanks again!

Answer 12

its okay! we have other methods to simplify the logic. Also, the simplification is fully automated... tools can do these pretty fast and optimally. so we dont have to do it manually, just knowing that it can be done manually is sufficient i feel ;)

Answer 13

What tools do you use? I was trying to force it through Wolfram Alpha, but either I made typos or I didn't know how to do it, or something... never really found the step by step solutions, even though I knew the final answer.

I agree 100% about knowing that manual is possible is sufficient for most work. I was trying to help someone who had to show all work on paper, and I wasn't "up to the task".

But if you have automated tool recommendations, I would be happy to keep them in mind for my next time on the topic.

Thanks again!

Answer 14

i dont think there exists a tool that shows the work step by step !

the tools i was referring are for optimizing digital logic like, design compiler etc