Question

Finite state machine (FSM) counter design: Gray codes have a useful property in that consecutive numbers differ in only a single bit position. Table 1 lists a 3-bit modulo 8 Gray code representing the numbers 0 to 7. Design a 3-bit modulo 8 Gray code counter FSM.

a) First design and sketch a 3-bit modulo 8 Gray code counter FSM with no inputs and three outputs, the 3-bit signal Q_2:0. (A modulo N counter counts from 0 to N − 1, then repeats. For example, a watch uses a modulo 60 counter for the minutes and seconds that counts from 0 to 59.) When reset, the output should be 000. On each clock edge, the output should advance to the next Gray code. After reaching 100, it should repeat with 000.

Clearly show your black box, state transition diagram, next state and output tables, your state encodings, next state and output equations, and circuit diagram.

b) Now add an UP input. If UP = 1, the counter advances to the next number (i.e., from 000→001, 001→011, etc.). If UP = 0, the counter retreats to the previous number (i.e., from 000→100, 100→101, 101→111, etc.). Go through all the steps of FSM design (1. Identify inputs and outputs 2. Sketch state transition diagram 3. Write state transition table 4. Select state encodings 5. Rewrite state transition table with state encodings 6. Write output table 7. Write Boolean equations for next state and output logic 8. Sketch the circuit schematic). Clearly label each part and finish with drawing the circuit that implements the FSM.

Table 1. Gray Codes Number Gray Code 001 011 010 110 2 4 101 100

Answer 1

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