Constructing a circuit from a Boolean expression

[Jim01]

Homework Statement

Construct a circuit from the Boolean equation:

Homework Equations

P v (~P ^ ~Q)

The Attempt at a Solution

According to the textbook, 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 that even though the outermost part of the expression is on the far left, it is where I begin. Is this correct? I come up with one OR gate, one AND gate and two NOT gates. I tried to draw this out using the keyboard but it doesn't format properly and so is incomprehensible. 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?

 

[Jim01]

Is there a way of adding gates to my thread? I attempted to cut and paste my Viso drawing but that didn't work. It is a lot easier to see the circuit rather than read and try to visualize it.

 

[jegues]

If you use the proper syntax, wolframalpha will provide with a picture of the logic gates as well as a truth table.

For example,

http://www.wolframalpha.com/input/?i=(x or y) and (x or !y)

 

[Jim01]

If you use the proper syntax, wolframalpha will provide with a picture of the logic gates as well as a truth table.

For example,

http://www.wolframalpha.com/input/?i=(x or y) and (x or !y)

Outstanding! Thank you for the information. After checking it I was right! I'm on the right track then. I was unsure whether or not I was interpreting the instructions correctly since most math has you doing everything inside the parenthesis first. It's counter-intuitive to do it last, so I was afraid I was misunderstanding.

Once again, thank you for your help.

 

[LCKurtz]

Of course you can make it simpler using the identity

a + a'b = a + b