Question

In: Electrical Engineering

Design a system with one input called “Up” such that when “Up” equals 1, the machine...

Design a system with one input called “Up” such that when “Up” equals 1, the machine counts 2, 3, 4, 5, 6, and repeat. If the “Up” input equals 0, the machine counts down 6, 5, 4, 3, 2, and repeat.

Show the State Transition Diagram, State Transition table, K-maps, and equations assuming JK flip flops and AND/OR/NOT combinational logic. Make sure to indicate on your State Transition Diagram what happens if the system initially is in one of the unused states (0, 1, or 7).

Solutions

Expert Solution

Input

Present State

Next State

JK Flip Flop Inputs

Up

Q2

Q1

Q0

Q2+

Q1+

Q0+

J2

K2

J1

K1

J0

K0

0

0

0

0

1

1

0

1

X

1

X

0

X

0

0

0

1

1

1

0

1

X

1

X

X

1

0

0

1

0

1

1

0

1

X

X

0

0

X

0

0

1

1

0

1

0

0

X

X

0

X

1

0

1

0

0

0

1

1

X

1

1

X

1

X

0

1

0

1

1

0

0

X

0

0

X

X

1

0

1

1

0

1

0

1

X

0

X

1

1

X

0

1

1

1

1

1

0

X

0

X

0

X

1

1

0

0

0

0

1

0

0

X

1

X

0

X

1

0

0

1

0

1

0

0

X

1

X

X

1

1

0

1

0

0

1

1

0

X

X

0

1

X

1

0

1

1

1

0

0

1

X

X

1

X

1

1

1

0

0

1

0

1

X

0

0

X

1

X

1

1

0

1

1

1

0

X

0

1

X

X

1

1

1

1

0

0

1

0

X

1

X

0

0

X

1

1

1

1

0

1

0

X

1

X

0

X

1

When Down Counting, i.e. Up = 0, then unused states 0,1,7 transits to state 6

When UP Counting, i.e. Up = 1, then unused states 0,1,7 transits to state 2

Excitation Table of JK Flip Flop

Q

Q+

J

K

0

0

0

X

0

1

1

X

1

0

X

1

1

1

X

0

LogiSim is used to design the circuit as per K-Map deduced equations for JK Flops.


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