Analysis of Synchronous Sequential Circuits

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Analysis of Synchronous Sequential Circuits
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Synchronous Sequential Circuits
Combinational Circuit
. ..
. ..
Y1
Flip Flops
. ..
. ..
Yr
Clock
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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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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(t1) D
• gt A(t1) AX BX
• B(t1) A'X

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Example Cont.

• Step 4 State Transition Table

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Timing Diagram

• Assume Input Sequence 00101110

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Example 2
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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
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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.