Chapter 15 - State Minimization-2x2(1)

Construct chart containing a square for each pair of

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Unformatted text preview: ows: 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 implied pair.) 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 added. 5. For each square i-j which does not contain an X, i ≡ j. Section 15.3 (p. 481) Equivalent Sequential Circuits Definition 15.2: 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 reduced table. 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 eq...
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