Question

There is an image of the operation of a Sequence Detector:

t نما 4 5 6 7 8 9 10 11 13 17 18 19 20 N 12 11 0 1 I OD 1 oo 0 14 15 16 0 0 0 O 1 1 1 1 0 O 11 0 11 0 1 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0

It is required to design, build and simulate the operation of the automata under the MEALY scheme:
1- Identify the sequence
2- Build the state diagram
3- Build the truth table considering FlipFlops JK
4- Get the logical functions using FlipsFlops JK
5- Draw the corresponding circuit

Answer 1

1) sequence:

Sequence detected by the sequence detector is 0110

2) State Diagram:

1. Identify the sequence. The sequence detected by the above Sequence detector is With overlapping 0110 ilo. olo 470 olo oll (SA S. 2) So I lo -> It has 5 stales n23 So an>5 > 23>5 So we need 3 flipflops to implement the Sequence Detector Encode the states = So 000 S --001 S2 - 010 33 - OU S4 - Too

3)Truth table

Present States Q1 input х Output Z Flipflop inputs J1 K1 Q0 Next states Q1* 0 Q0* J2 K2 JO Q2 0 KO Q2* 0 0 0 0 1 0 0 х 0 X 1 х 0 0 0 1 0 0 0 0 0 х 0 0 х 0 0 1 0 0 0 1 0 0 х 0 х X 0 0 0 1 1 0 1 0 0 0 х 1 1 0 0 0 0 0 1 0 0 х 1 1 х 1 1 0 0 1 0 1 1 0 0 х X 0 1 х 0 1 1 0 1 0 0 1 1 х х 1 X 1 0 1 1 1 0 0 0 0 0 х х 1 1 1 0 0 0 1 0 0 0 х 0 0 X 0 х 1 0 0 0 1 0 0 х 1 1 х 0 х 1 0 1 0 X х х х х х х х х х 1 0 1 1 х х х х х х х х х х 1 1 0 X х х х х х х х х х 0 0 1 1 1 х х х х х х х х х х 1 1 1 0 х X х х х х х х х х 1 1 1 1 х х х х х X х х х х

4) logical functions:

-> K-Maps for Input Equations. 1) Ja Qox 10 00 O G o 110 11 y X x x X < X Ja 9) K2 QoX 029, ou os 10 x X X 01 x х x X 11 X X X Х x X 10 K2 = x

3) J 00 ol 11 lo OD 0 - 0 이 x Х x х x x x 10 0 U J = Q₂X + QoX 4) K Qox COOL21 8 x gx X 00 ol o X 11 X x х x X 10 > ㅈ = Q,+Q, QO

5) Jo Qor 11 х Х X х X X X X J. QI Go + Qx 6) ko QoX 00 01 1 10 00 x O x x - X " к X 10 x x x x ko =Q,+ QoX

1) Output z 10 06 | 0 o o o o o u X X X x 2 = Q, QOT 10 0 x х

5) Corresponding Circuit:

X Q2 Kleno JK2 Q2 Q1 0 Kieno JK1 QO 0 Keno QO' JKO

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