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# Homework 8 minimal state table

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Homework 8
Max marks: 120

Problem 1 Derive a minimal state table for an
FSM (Finite-state machine) that acts as a threebit parity generator. For every three bits that are
observed on the input w during three consecutive
clock cycles, the FSM generates the parity bit p =
1 if and only if the number of 1s in the three-bit
sequence is odd (10 marks) [1, Prob 6.12].
Problem 2 Design a modulo-6 counter, which
counts in the sequence 0, 1, 2, 3, 4, 5, 0, 1, .
. . . The counter counts the clock pulses if its
enable input, w, is equal to 1. Use D flip-flops
in your circuit (20 marks) [1, Prob 6.23].
Problem 3 Design a three-bit counterlike circuit controlled by the input w. If w = 1, then the
counter adds 2 to its contents, wrapping around
if the count reaches 8 or 9. Thus if the present
state is 8 or 9, then the next state becomes 0 or
1, respectively. If w = 0, then the counter subtracts 1 from its contents, acting as a normal
down-counter. Use J-K flip-flops in your circuit
(20 marks) [1, Prob 6.26].
State Reduction
Problem 4 Reduce the following state table to
a minimum number of states:
(10 marks).
Problem 5 Digital engineer B. I. Nary has
just completed the design of a sequential circuit
which has the following state table:
His assistant, F. L. Ipflop, who has just completed this course, claims that his design can be
used to replace Mr. Nary’s circuit. Mr. Ipflop’s
design has the following state table:
2. If Mr. Nary’s circuit is always started in
state S0 , is Mr. Ipflop correct? (Prove your
answer by showing equivalent states, etc.)
(10 marks)
.
State Assignment
Problem 6 1. Reduce the following state table to a minimum number of states using
1
implica- tion charts (10 marks).
2. Use the guideline method to determine a
suitable state assignment for the reduced table (10 marks).
3. Realize the table using D flip-flops (10
marks).
4. Realize the table using J-K flip-flops (10
marks).
References
 S. Brown and Z. Vranesic. Fundamentals of
Digital Logic with Verilog Design: Third Edition. McGraw-Hill Higher Education, 2013.
2 Homework 8 minimal state table
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