Analyzing our example circuit

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Presentation transcript:

Analyzing our example circuit A basic state table for our example circuit is shown below. Remember that there is one input X, one output Z, and two flip-flops Q1Q0. The present state Q1Q0 and the input will determine the next state and the output. Sequential circuit analysis

Output at the current time The outputs are easy The output depends on the current state – Q0 and Q1 – as well as the inputs. From the diagram, you can see that Z = Q1Q0X Output at the current time Sequential circuit analysis

Step 1: Flip-flop input equations For our example, the flip-flop input equations are: J1 = X’ Q0 K1 = X + Q0 J0 = X + Q1 K0 = X’ JK flip-flops each have two inputs, J and K. (D and T flip- flops have one input each.) Sequential circuit analysis

Step 2: Flip-flop input values With these equations, we can make a table showing J1, K1, J0 and K0 for the different combinations of present state Q1Q0 and input X. J1 = X’ Q0 J0 = X + Q1 K1 = X + Q0 K0 = X’ Sequential circuit analysis

Step 3: Find the next states Finally, use the JK flip-flop characteristic tables or equations to find the next state of each flip-flop, based on its present state and inputs. The general JK flip-flop characteristic equation is: Q(t+1) = K’Q(t) + JQ’(t) In our example circuit, we have two JK flip-flops, so we have to apply this equation to each of them: Q1(t+1) = K1’Q1(t) + J1Q1’(t) Q0(t+1) = K0’Q0(t) + J0Q0’(t) We can also determine the next state for each input/current state combination directly from the characteristic table. Sequential circuit analysis

Sequential circuit analysis Step 3 concluded Finally, here are the next states for Q1 and Q0, using these equations: Q1(t+1) = K1’Q1(t) + J1Q1’(t) Q0(t+1) = K0’Q0(t) + J0Q0’(t) Sequential circuit analysis

Getting the state table columns straight The table starts with Present State and Inputs. Present State and Inputs yield FF Inputs. Present State and FF Inputs yield Next State, based on the flip- flop characteristic tables. Present State and Inputs yield Output. We really only care about FF Inputs in order to find Next State. Note: the outputs occur this cycle and the next state in the next cycle Sequential circuit analysis

Sequential circuit analysis State diagrams We can also represent the state table graphically with a state diagram. A diagram corresponding to our example state table is shown below. input output 00 01 10 11 1/0 0/0 1/1 state Sequential circuit analysis