# Clocked synchronous sequential circuit: find input and output equations?

#### Gonzalo Armbrust

Joined Jun 28, 2015
16
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)?

#### #12

Joined Nov 30, 2010
18,210
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.

#### Gonzalo Armbrust

Joined Jun 28, 2015
16
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?

#### #12

Joined Nov 30, 2010
18,210
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. #### WBahn

Joined Mar 31, 2012
25,760
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.