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Last updated: 11/4/2006
ECEn/CS 224
Chapter 17 Homework Solutions
17.1
Design the FSM of Figure 16.5 using a onehot encoding and reduce the design to gates.
Recall that with the onehot encoding we can easily design the FSM directly from the
state diagram, without resorting to transition tables or Kmaps. Since there are four states,
we need four flip flops. Call the outputs of the flip flips S0, S1, S2, and S3,
corresponding the respective states.
By inspection of the state diagram, we obtain the following nextstate logic:
NS0 = S0•Xin + S3•Xin = Xin•(S0 + S3)
NS1 = S0•Xin’ + S1•Xin’ + S2•Xin’ + S3•Xin’ = Xin’•(S0+S1+S2+S3) = Xin’
NS2 = S1•Xin
NS3 = S2•Xin
Notice that by factoring, we can reduce the number of gates required for NS0 without
increasing the number of logic levels. Also, we were able to reduce NS1 to Xin’ since we
know that, with a onehot encoding, exactly one of the state bits will be high at any given
time. You can also come to this same result by observing that the Xin’ condition always
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 Spring '10
 Schultz
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