A student writes:

     Dr. Patt,
      I'm working on problem 6 of set 2...I have some of my AND
     array going into an OR function, and the other ANDs are not
     connected to the OR array...which I think is right because
     that is how you drew the adder, maybe i'm obsessive compulsive,
     but should I connect the rest of the array to a NOR gate or just
     leave them alone?
      << name withheld to protect the self-proclaimed obsessive compulsive >>


and there was no PS, so I guess the obsessive compulsive decided not to add whatever it was...

Anyhow, I am delighted to get this question because it gives me another chance to reinforce what is going on. Thank you!

Each of the AND gates in the logic circuit provides an output 1 for exactly one input combination. If that AND gate's output is connected to an input of the OR gate, then the corresponding input combination will produce a 1 at the output of the OR gate.

Let's take an example of an input combination that produces an output 0 in the TRUTH TABLE. We want that input combination to produce a 0 at the output of the OR gate. If we SIMPLY do not connect the corresponding AND gate to the OR gate, what will happen? When that input combination is present, the output of that AND gate will be a 1. BUT it will not be connected to the OR gate. Furthermore, when the output of that AND gate is a 1, the outputs of all the other AND gates are 0. (Do you see why?) Since all the gates that are connected to the OR gate have 0 as their input to the OR gate, the output of the OR gate is 0. ...which is what you want.

Therefore, it is not necessary to do anything with those AND gates that correspond to input combinations that produce 0. Not connecting them to the OR gate is sufficient.


Good luck with the rest of the problem set.

Yale Patt