Constructing circuit from Boolean expression

[Jim01]

I must construct a circuit from the following Boolean expression:

P v (~P ^ ~Q)

From my understanding I am supposed to go from right to left, working on the outermost part of the expression to the innermost part. I read this as saying even though the outermost part of the expression is on the right, that is where I begin. Is this correct? I come up with one OR gate, one AND gate and two NOT gates. Here is what I came up with:


P goes into a NOT and comes out ~P. ~P goes into AND and comes out ~P ^ Q.
P goes into OR and comes out P v (~P ^ ~Q)

Q goes into NOT and comes out ~Q. ~Q goes into AND and comes out ~P ^ Q.

~P ^ Q goes into OR and comes out P v (~P ^ ~Q)

Am I on the right track?

 

[phinds]

I've never heard of a system where you do not evaluate inside of parentheses first

 

[Jim01]

I've never heard of a system where you do not evaluate inside of parentheses first

Well that's definitely always been the case in the past but I quoted from the book verbatim. "Go from the right side of the diagram to the left, working from the outermost part of the expression to the innermost part."

The example used was (~P ^ Q) v ~Q

In the above case they began with the v first.

 

[Jim01]

I just noticed this disclaimer: "This forum is not for homework or any textbook-style questions." I did not see this before. I will post my question in the appropriate section. Please pardon my mistake.

 

[blue_raver22]

I cannot confirm if you are on the right track without seeing the specific circuit you have constructed. However, your approach of using one OR gate, one AND gate, and two NOT gates is correct. You have correctly applied the laws of Boolean algebra to simplify the expression and construct the corresponding circuit. It is important to note that there are multiple ways to construct a circuit from a Boolean expression, so as long as your circuit accurately represents the given expression, it can be considered correct. It is also important to double check your work and ensure that all inputs and outputs are correctly connected in the circuit.