homework 12 digital control PDF

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homework 12 digital control...

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Assignment #12 --------------------------------------------------------------------------------------------------------------------------------------1. [8 pts] A Gray Code is a binary code with the property that exactly one bit changes from each position to the next. An excellent example of a 2-bit Gray Code is the header column (or header row) on a 4-bit Karnaugh Map: 00, 01, 11, 10. Gray Codes occasionally arise in specialized situations such as positional encoders, error correction in digital communications and many more. You are to design a 3-bit Gray Code counter that starts counting at 000 and keeps counting up. Use positive edge triggered D-type flip-flops to design the counter. a. Derive the truth table consisting of current states of the counter (QN QN-1 …Q0) as the inputs and next states of the counter (DN DN-1 … D0) as outputs. Show the complete truth table. b. Derive the equations for each driving CLN. Minimize them (using any approach) as much as you can. Show your work! c. Draw the final schematic using D-type flip flop. Label all flip-flops and I/O. d. Draw the timing diagram for the schematic obtained in Part c above. The timing diagram should cover all the possible state transition mentioned in the problem statement. Please draw timing diagram on a separate sheet of paper as part of your homework submission. Assume all Q N’s to be ‘0’ to begin with. NOTE: Include following signals in your timing diagram i.e., CLK, all the Q’s and all the D’s. -------------------------------------------------------------------------------------------------------------------------------------2. [4 pts] Consider the following state transition table: Input

Current state

Next state

Outputs

Is X a Mealy or Moore output?

Justify your answer

Is Y a Mealy or Moore output?

Justify your answer

--------------------------------------------------------------------------------------------------------------------------------------3. [8 pts] Consider the State Transition Diagram shown below consisting of four states (S0, S1, S2 and S3) and the signals V, W, X, Y and Z. Answer the following questions regarding the State Transition Diagram: Note: Due to graphical program X’ = not X.

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a. Which signals are inputs? b. Which signals are outputs? c. For each output, identify if it is a Moore or Mealy output? d. For each state, identify if it is complete. Is the overall state transition diagram complete? Justify your answer. ---------------------------------------------------------------------------------------------------------------------------------------

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Answers: 1. a. Q2 0 0 0 0 1 1 1 1

b.

Q1 0 0 1 1 0 0 1 1

,

Q0 0 1 0 1 0 1 0 1

D2 0 0 1 0 0 1 1 1

,

c. d. 2. X = Moore, Y = Mealy 3. a. X, Y b. V, W, Z c. d. No

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D1 0 1 1 1 0 0 1 0

D0 1 1 0 0 0 0 1 1...