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CSM51Asolution_chapter8

# The system has two inputs x the variable to be

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Unformatted text preview: K1 = xQ0 K0 = x z2 = Q2 + Q1Q0 z1 = Q1 + Q2Q00 z0 = Q1 + Q02Q0 The sequential network is shown in Figure 8.31. A comparison of the networks of Figures 8.30 and 8.31 indicates that solution a results in a simpler network. A modulo-7 up down counter requires seven states. Since the counter is binary, the state assignment is speci ed. The system has two inputs: x the variable to be counted, and c, to control up c = 1 or down c = 0 counting. The state table is Input PS x = 0 x = 1down x = 1up 000 000 110 001 001 001 000 010 010 010 001 011 010 100 011 011 100 100 011 101 101 101 100 110 110 110 101 000 NS = z Exercise 8.28 Solutions Manual - Introduction to Digital Design - February 22, 1999 153 J CK 0 K CK x Q1 Q0 Q2 Q J CK 1 Q J CK 2 Q Q’ K Q’ K Q’ z2 Q2 Q0’ Q1 z1 Q2’ Q0 Q1 z0 Figure 8.31: Network for Exercise 8.27 b a Based on the excitation function for a T ip- op we obtain the following table for ip- op inputs: Input PS Q2Q1 Q0 x = 0 x = 1down x = 1up 000 000 110 001 001 000 001 011 010 000 011 001 011 000 001 111 100 000 111 001 101 000 001 011 110 000 011 110 From K-maps we obtain: T2 T1 T0 The network is shown in Figure 8.32. b using D-type ip- ops the next state is given as input, Qt + 1 = Dt, so the rst table shown in this exercise is used. This time, the next state bits for the case x = 0 have values di erent than zero, and for this reason we need to consider the cases x = 0 and x = 1 separately. Let the inputs of the D-type FFs be D2 ; D1 , and D0 . For the case x = 1, using K-maps, we obtain: D2 x = 1 = Q2 Q0 + Q1 Q0c + Q2 Q01c + Q2 Q1 c0 + Q02 Q01 Q00c0 D1 x = 1 = Q01 Q00 c0 + Q01 Q0 c + Q1 Q0c0 + Q02Q1 Q00 c D0 x = 1 = Q2 Q01 Q00 + Q02 Q00 c + Q1Q00 c0 For x = 0 the expressions for Di are: D2 x = 0 = Q2 D1 x = 0 = Q1 D0 x = 0 = Q0 T2 = xcQ1 Q0 + cQ2 Q1 + c0 Q01 Q00 T1 = xcQ0 + Q2 Q1 + c0 Q00 = xc  Q00  + Q2Q1  T0 = xc + Q2 + Q1 + Q0c0 + Q02 + Q01  154 Solutions Manual - Introduction to Digital Design - February 22, 1999 Combining both cases we obtain the...
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