So i have been given the following circuit ( see attached) to find the input and output equations, only i'm confused about it since there really isn't an output in the circuit, just the "next state", given that the output equations are T(B) = B+ (Ta)' and T(A) = Ta + Tb ( T corresponds to the respective flop flop), would the "output equations" simply be just the input equations, only they are dependent on the clock ( since the T flip flop would toggle)?

 

I would start with a Truth Table. Assume B prime is "0" and list what is the state of A, A prime, and B.
Then do that for B prime is "1".
By the time you get done with that, you will understand what happens each time the clock flops.

 

I would start with a Truth Table. Assume B prime is "0" and list what is the state of A, A prime, and B.
Then do that for B prime is "1".
By the time you get done with that, you will understand what happens each time the clock flops.

wouldn't B' just be the compliment of B? I could make a truth table consisting of A and B, and then the next state of A and B right?

 

As far as I know, you're right, but I'm an analog designer. I have to look up every digital chip that gets in my way.

 

Defining an output is pretty easy -- your output is (A,B). What you have a harder time doing is defining an input. This is what is known as a free-running circuit. As a result, one way to look at it is that your "inputs" are also (A, B).

The next state of A will be a function of A and B. Similarly, the next state of B will be a function of A and B. I think those are the equations you seek.