Chapter 15 - State Minimization-2x2(1)

Section 156 p 484 1 assign flip flop state values to

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Unformatted text preview: uations from the maps. Section 15.6 (p. 484) 1. Assign flip-flop state values to correspond to the states in the reduced table. 2. Construct a transition table which gives the next states of the flip-flops as a function of the present states and inputs. 3. Derive the next-state maps from the transition table. Figure 15-9a: Next- State Maps for Table 15-6. Table 15-6 X 4. Find flip-flop input maps from the next-state maps using the techniques developed in Unit 12 and find the flipflop input equations from the maps. Figure 15-9b: Next- State Maps for Table 15-6 Table 15-7: Represents a sequential circuit with two inputs (X1 and X2) and two outputs (Z1 and Z2). Figure 15-10: Next- State Maps for Table 15-7 Figure 15-11: Derivation of S-R Equations for Table 15-7 Equivalent State Assignments After state minimization => assign flip-flop states to correspond to the states in the table. Given a sequential circuit with three states and two flipflops (A and B), there are 4 × 3 × 2 = 24 possible state assignments for the three states. The logic required to realize a sequential design depends on the way this state assignment is made. Table 15-8. State Assignments for 3-Row Tables Section 15.7 (p. 487) If flop has both Q and Q' as outputs ("symmetrical"), complementing one or more columns of a state assignment will have no effect on the cost of realization. Note: if asymmetrical flip-flops are used (e.g., a D flipflop), complementing a column may require adding an inverter to the circuit. Figure 15-12: Equivalent Circuits Obtained by Complementing Qk Table 15-9. Figure 15-13: Equivalent Circuits Obtained by Complementing Qk When realizing three-state sequential circuit with symmetrical flip-flops, it is only necessary to try three different states to be assured of a minimum cost realization. Similarly, only three different assignments must be tried for four states. A3 and B3 differ in col order, C3 is complement of A3 JK Flip-Flops Assignment A J1 = X Q2'; K1 = X'; J2 = X Q1'; K2 = X; Z = X' Q1 + X Q2; Assignment B J2 = X Q1'; K2 = X'; K1 = X; K1 = X Q2; Z = X' Q2 + X Q1; Assignment C K1 = X Q2; J1 = x'; K2 = X' Q1'; J2= X; Z = X' Q1' + X Q2‘; D flip-flops Assignment A D1 = X Q2'; D2 = X Q1'; Assignment B D1 = X' + Q2'; D2 = X'(Q1+ Q2); Assignment C D1 = X'(Q2 + Q1); D2 = X + Q1 Q2...
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This document was uploaded on 03/16/2014 for the course EE 316 at University of Texas at Austin.

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