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Unit 16 Solutions
16.30 (b) First, assign LC = Q1, LB = Q2, LA = Q3, RA = Q4, RB = Q5, RC = Q6. So S0 = 000000, S1 = 001000, S2 = 011000, etc.
This state machine has too many state variables to use Karnaugh maps. Instead, we will write down equations for
each ip-op by inspection.
First consider Q1. Q1 = 1 in states S3 or S7 only.
I. (S0, S1, S2, S3, S4, S5, S6) for S7 in LRH = 001, 011, 101
(S1, S2, S3, S6, S7) for S0 in LRH = 010
(S3, S4, S5, S6, S7) for S0 in LRH = 100
II. Every state matches S0 and S7. But S0 and S7 match the best, so (S0, S7)×(many times)
III. (S1, S2, S3, S7) (S4, S5, S6, S7) etc.
From LogicAid:
16.30 (c) State LRH = 000 001 010 011 100 101 110 111 LC LB LA RA RB RC
S0 S0 S7 S4 S7 S1 S7 - - 0 0 0 0 0 0
S1 S0 S7 S0 S7 S2 S7 - - 0 0 1 0 0 0
S2 S0 S7 S0 S7 S3 S7 - - 0 1 1 0 0 0
Q1
Q2 Q30 1
00
01
11
S0
S2
S6
S7
S3
S5