Digital Circuit Help (Custom Logic Gates)

[JMoxey]

Hello everyone!

I am currently stuck on a digital systems homework question. We are given a custom logic gate with a truth table (its effectively an AND gate where one of the inputs have a NOT gate). With this logic gate and truth table, we are told that we can build any combinational logic function and we have to show this by building 2-input AND gates, 2-input OR gates, and a NOT gate from the custom logic gate and truth table given (Figure 1).

Figure 1 - The custom logic gate, and truth table. ​

I have figured out how to build the 2-input AND gate (Figure 2), although I have no idea where to start on building the 2-input OR gate and the NOT gate. I spent 2 hours trying to figure out how to build the OR gate but couldn't figure it out! And I was stumped as to how you would build a NOT gate as it only has one input, and if the input is 0, the output would always be 0 no matter how many of these custom logic gates you had, and the way you had them circuited. I had no clue how you could turn the 0 input into a 1 by these logic gates??

Figure 2 - The 2-input AND gate I built from the custom logic gates.
​

Can anyone guide me on where to start with building the 2-input OR and NOT gates? I'm stumped!
Thanks!

 

[ramussons]

Hint:
What is the expression for Z in terms of A and B from the Truth Table?

Recall DeMorgan's Theorems.

 

[KrisBlueNZ]

Hi there and welcome to Electronics Point

That assignment does have an answer. I guess you're not looking at it the right way.

Start by studying the truth table of that gate they've given you. What can you make it do? What happens if you connect the inputs together? That would be the first and fourth lines of the truth table. The output will always be low. Not very useful. What happens if you tie input A high? That's the third and fourth lines. Again, the output is always low.

But what happens if you tie input A low and just consider input B and the output? What is the truth table for the single-input gate you end up with? And what if you tie input B high or low and use A as the gate input?

That should get you started!