Analysis of Synchronous Sequential Circuits 692021 A Berrached

Analysis of Synchronous Sequential Circuits 6/9/2021 A. Berrached 1

Synchronous Sequential Circuits X 1 X 2 Xn . . Combinational Circuit . . Y 1 Yr Flip Flops Z 1 Zm . . Clock 6/9/2021 A. Berrached 2

Synchronous Sequential Circuits • Zi = fi(X 1, X 2, …, Xn, Y 1, Y 2, …, Yr, ) • Yi = gi(X 1, X 2, …, Xn, Y 1, Y 2, …, Yr, ) 6/9/2021 A. Berrached 3

Synchronous Sequential Circuits 1. Derive the output equations 2. Derive the F/Fs input equations 3. Derive the next state equations 4. Derive the CKT's State Transition Table State table give a complete description of circuits behavior 5. State diagram 6. Get timing diagrams 6/9/2021 A. Berrached 4

Example 1 6/9/2021 A. Berrached 5

Example 1 Cont. Step 1: Z = AX' + BX' Step 2: DA = AX + BX DB = A'X Step 3: D F/F characteristic eq. Q(t+1) = D ==> A(t+1) = AX + BX B(t+1) = A'X 6/9/2021 A. Berrached 6

Example Cont. Step 4: State Transition Table 6/9/2021 A. Berrached 7

Timing Diagram Assume Input Sequence: 00101110 6/9/2021 A. Berrached 8

Example 2 6/9/2021 A. Berrached 9

Example 2: Analysis Preliminary: inputs: X outputs: Z State Variables: A & B Note: Moore circuit (1) output equations: Z = AB' (2) Flip Flop Input Equations: JA = B KA = BX' JB = X' KB = AX' + A'X 6/9/2021 A. Berrached 10

State Transition Table 6/9/2021 A. Berrached 11

Traffic Light Controller • You are to design a traffic light controller to control an intersection. The intersection consists of two streets, one running north-south (called NS) and the other running eastwest (called EW). The circuit has to control one traffic lights on the NS street, one traffic light on the EW street. • Each of the traffic signals consists of a red, yellow, and green light. Each of the traffic signals cycles through red, green, yellow, and back to red. When one traffic signal is green or yellow, the other is red. When one traffic light is red, the other is greed or yellow. To simplify the design and shorten the experimentation time, we will set the green, yellow, and red time periods to 4, 1, and 5 seconds, respectively. 6/9/2021 A. Berrached 12

Simple Serial Lock • Design a digital lock. Assume only four digits can be entered 0, 1, 2, and 3. • Lock will open when the following sequence of digits is entered, in order: 3, 1, 2, 1. 6/9/2021 A. Berrached 13