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1. Construct chart containing a square for each pair of states.
2. Compare each pair of rows in the state table:
If the outputs associated with states i and j are different, place an X in
square i-j to indicate that i /≡ j.
If the outputs are the same, place the implied pairs in square i-j.
(If the next states of i and j are m and n for some input x, then m-n is an
If the outputs and next states are the same (or if i-j only implies itself), place
a check (√) in square i-j to indicate that i ≡ j. 3. Go through the table square-by-square. If square i-j contains the implied
pair m-n, and square m-n contains an X, then i /≡ j, and an X should be
placed in square i-j.
4. If any X’s were added in step 3, repeat step 3 until no more X’s are
5. For each square i-j which does not contain an X, i ≡ j. Section 15.3 (p. 481) Equivalent Sequential Circuits
Sequential circuit N1 is equivalent to sequential circuit N2 if
for each state p in N1, there is a state q in N2 such that p ≡ q,
and conversely, for each state s in N2, there is a state t in N1
such that s ≡ t. Section 15.4 (p. 481)
Figure 15-6: Graphs for Equivalent Circuits Incompletely Specified State Tables
Assume that A can only generate two possible output
sequences, X = 100 and X = 110. Thus B has only two possible
input sequences. Also, C only reads Z during everything third
input. Figure 15-8 Figure 15-7: Implication Tables for Determining Circuit Equivalence
Table 15-5. Incompletely Specified State Table Derivation of Flip-Flop Input Equations
After state minimization, use the following procedure to get flip-flop
input equations: 1. Assign flip-flop state values to correspond to the states in the
2. Construct transition table for next states of the flip-flops as
function of the present states and inputs.
3. Derive the next-state maps from the transition table.
4. Find flip-flop input maps from the next-state maps using the
techniques developed in Unit 12 and find the flip-flop input
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- Spring '08