Analysis of Synchronous Sequential Circuits

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Analysis of Synchronous Sequential Circuits

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Synchronous Sequential Circuits

Combinational Circuit

Flip Flops

Clock

X1

X2

Xn

Z1

Zm...

...

......Y1

Yr

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Synchronous Sequential Circuits

• Zi = fi(X1, X2, …,Xn, Y1, Y2, …,Yr, )

• Yi = gi(X1, X2, …,Xn, Y1, Y2, …,Yr, )

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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

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D

C

Q

D

C

Q

A

B

Z

X

Example 1

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Example1 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

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Example Cont.

Step 4: State Transition Table

Present State Input Next State OutputA B X A+ B+ Z

0 0 00 0 10 1 00 1 11 0 01 0 11 1 01 1 1

0 0 00 1 00 0 11 1 00 0 11 0 00 0 11 0 0

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Timing Diagram

Assume Input Sequence: 00101110

Z

B

A

X

Clock

200 400

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Example 2

J

K

Q

Q

J

K

Q

Q

A

X

B

Z

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Example2: 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

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State Transition Table

Present State Input JK Input Next State OutputA B X Ja Ka Jb Kb A+ B+ Z

0 0 00 0 10 1 00 1 11 0 01 0 11 1 01 1 1

0 0 1 0 0 1 00 0 0 1 0 0 01 1 1 0 1 1 01 0 0 1 1 0 00 0 1 1 1 1 10 0 0 0 1 0 11 1 1 1 0 0 01 0 0 0 1 1 0

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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 east-west (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.

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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.