ECE 102 - Homework 12
Due 12/08/2017

This is the last homework assignment. Turn in the solutions to all the problems.

[Note: In calculating the final homework grade,  your two lowest homework scores will be dropped. ]
  1. A single input (X), single output (Z) circuit produces an output of 1 for every second one it receives and for every second 0 it receives.
    a) Design a Mealy sequential circuit with minimum number of states using J-K flip-flops. 
    b) Draw a Moore state diagram  with minimum number of states for the circuit.

  2. A finite state machine has three inputs (A2,A1,A0) and one output (Z). The output becomes one if and only if the the current value of the binary number (A2,A1,A0) exactly divides the binary number that occurred previously on (A2,A1,A0).  Consider 000 to be divisible by any 3-bit pattern, and no 3-bit pattern to be divisible by 000.Draw a Mealy state diagram with the minimum number of states to implement this function.How many states will be required to implement this using a Moore state diagram.
  3. Consider the following Moore type state transition table.  X,Y are inputs, and Z is the output. Identify the equivalent states, and provide the state transition table and the state diagram with the  minimum number of states.

    Present
    State

    		 Next State
    		 Output
      Z
    XY=00
    		 XY=01
    		 XY=10
    		 XY=11
    A
    		 D
    		 E
    		 A
    		 C
    		 1
    B
    		 A
    		 E
    		 D
    		 E
    		 1
    C
    		 B
    		 F
    		 E
    		 A
    		 0
    D
    		 B
    		 C
    		 B
    		 C
    		 1
    E
    		 A
    		 F
    		 C
    		 D
    		 0
    F
    		 D
    		 A
    		 F
    		 B
    		 0


  4.  Consider the following Mealy type state transition table.  Use an implication table to identify the equivalent states, and provide an equivalent state transition table and the state diagram with the  minimum number of states.

    Present
    State
    		 X=0
    		 X=1
    Next
    State
    		 Output
    Z
    		 Next
    State
    		 Output
    Z
    A
    		 C
    		 0
    		 B
    		 1
    B
    		 D
    		 0
    		 E
    		 1
    C
    		 D
    		 1
    		 G
    		 1
    D
    		 B
    		 0
    		 E
    		 1
    E
    		 G
    		 0
    		 F
    		 1
    F
    		 B
    		 1
    		 H
    		 1
    G
    		 I
    		 1
    		 H
    		 0
    H
    		 I
    		 1
    		 G
    		 0
    I
    		 A
    		 1
    		 A
    		 0



  5. A single input (X) single output (Z) circuit should transmit its input to the output, except that it should prevent the sequence 00110 from occurring at the output.  So Z is the same as X, except that if the pattern 00110 occurs at X, the output Z should be 1 rather than 0 for the last 0 of the pattern.  The sequence 00110 is therefore replaced by 00111 in the output.   Draw a Mealy state diagram for the circuit.


  6. A Mealy type sequential circuit and its implementation based on two J-K flip-flops and a ROM is given below. The states in the transition diagrams are labeled PQ. For example, the state corresponding to P=0, Q=1 is denoted as 01.  The input to the sequential circuit is X and its output is Z. Draw a complete state transition diagram for the circuit.
    ROM Contents:

    A2 A1 A0

     D0 D1 D2 D3 D4

    0  0  0

     0  0  1  0  1

    0  0  1

     1  0  1  0  0

    0  1  0

     1  1  0  1  0

    0  1  1

     1  1  0  1  0

    1  0  0

     0  0  0  1  1

    1  0  1

     1  0  0  0  0

    1  1  0

     0  1  1  1  1

    1  1  1

     0  1  1  0  0

    Circuit:


    © A.Jayasumana, Colorado State University