# Exclusive- OR and AND gates

#### Gigantic Turkey

Joined Jan 14, 2013
10
My homework asks me to implement a boolean function with exclusive-OR and AND gates. I have to use the minimum number of inputs which means converting to XOR. Not really knowing how to proceed, I have made a k-map to plot it so I understand it better, and made tables with all the rules, but I honestly don't know how to do the conversion so I don't even know how to start. I have a great textbook, but it doesn't show such a complicated example as what is assigned. I have googled the method of conversion, but nothing really shows examples for more than 3 variables, and I am using up to 4. I am assuming I need to make a diagram with the gates, but since I cannot figure out how to convert to XOR I'm dead in the water. Please guide me. I've been on this for several days and I am begging for help. Due tomorrow. Thank you. GT

The function is WXY'Z + WZ' + W'Z

#### WBahn

Joined Mar 31, 2012
25,923
You didn't say how many inputs your XOR and AND gates had. Do you only have 2-input gates to work with?

First off, any solution is better than no solution, so don't worry about getting the minimum number of inputs.

Q1) If you had nothing but inverters, 2-input AND gates, and 2-input NAND gates, what would your circuit look like?

Q2) Can you replace your inverters with XOR gates? (i.e., do you know how to make in inverter out of an XOR gate?)

Q3) Now you just need to figure out how to make an OR gate out of AND gates and inverters. Do you know how to do that? Hint -- DeMorgan's.

At this point you can build a solution that uses only 2-input XOR and AND gates. Then you can start figuring out how to squeeze as many inputs from your circuit as you can.

And kudos to your instructor for specifying what metric is to be used to determine the quality of the solution.

#### Gigantic Turkey

Joined Jan 14, 2013
10
Thank you for your reply. I don't have an answer to your very first question. I was not given that information. This question is pulled directly from the textbook so I know I need to refer to the book for help. I do not know how to make an invertor out of an XOR gate so perhaps that is why I feel so lost. I will study up on DeMorgan's. We were told that we would not be tested on that so I didn't put my energy into it.

I need to do as you suggest and build a solution that uses only 2-input XOR and AND gates. However, I don't know what that looks like so I just don't know how to start. I think once I get going I can do it, I just need some guidance on how to begin. I look forward to the day that I look back and think "that was so easy". Right now, it seems like an enormous hurdle.

#### WBahn

Joined Mar 31, 2012
25,923
I actually mistyped my first question. I meant to ask, "What would it look like if you only had inverters, 2-input AND gates and 2-input OR gates?"

As for making an inverter out of an XOR gate, look at the truth table and recognize that your inverter only has one input, so pick one of the XOR inputs as your inverter input. Let's say you pick A. So what do you do with B? Well, can you see what B has to be so that the output will always be A'?