CSM51Asolution_chapter8

22 s01 s10 ns z s1 1 s2 0 s3 0 s0 0 s5 0 s1 0 s20 s50

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Unformatted text preview: P5 = A F;2H  C  E G B;6D 5 11 2 3 6 44 1 P2 = A  F; H  2  B; C; D; E; G 3 P6 = P5 = fA; E ; C ; F; H ; G; B; Dg The reduced state table is PS A = S0 E  = S1 C  = S2 F; H  = S3 G = S4 B; D = S5 The state diagram is shown in Figure 8.22. S0/1 S1/0 NS z S1 1 S2 0 S3 0 S0 0 S5 0 S1 0 S2/0 S5/0 S4/0 S3/0 Figure 8.22: State diagram for Exercise 8.19 The network in its equilibrium state produces a 1 every six clock pulses, that is, it implements a modulo-6 frequency divider. Exercise 8.20 The expressions for the ip- op inputs are: The transition table is TA = QA + QB TB = Q0A + QB 142 Solutions Manual - Introduction to Digital Design - February 22, 1999 PS FF inputs NS QAtQB t TAtTB t QAt + 1QB t + 1 00 01 01 01 11 10 10 10 00 11 11 00 Let us de ne the following encoding: QAQB 00 01 10 11 S0 S1 S2 S3 S1 S2 S0 S0 The resulting state table is PS NS S0 S1 S2 S3 The state diagram is shown in Figure 8.23. The network implements an autonomous modulo-3 counter. S0 S1 S2 S3 Figure 8.23: State diagram for Exercise 8.20 Exercise 8.21 The expressions for the ip- op inputs and for the output are S2 R2 J1 K1 T0 z = = = = = = xQ01 + xQ02 Q00 Q2 Q 1 Q0 x0 + Q2  Q0 + Q2 x0 + Q2 + Q1 Q02 + Q01 + Q0 x + Q02 + Q1 + Q00  Q02  Q1 x0 Q00  + Q01 x0 Q0  + Q2  Q1 xQ00  + Q1 xQ0  The transition table is Solutions Manual - Introduction to Digital Design - February 22, 1999 143 Q2 Q1 Q0 000 001 010 011 100 101 110 111 PS 00 00 00 00 00 00 01 01 x=0 00 11 00 11 01 11 01 11 Input 1 1 1 1 1 0 0 1 10 10 10 00 10 10 01 01 x=1 00 01 00 01 01 11 01 11 S2R2 J1 K1 T0 Q2 Q1Q0 000 001 010 011 100 101 110 111 0 0 1 1 1 1 0 1 Input x=0 x=1 001,1 100,0 010,1 101,0 011,0 111,1 000,0 000,1 101,0 101,1 111,1 110,0 000,1 000,0 000,0 000,1 NS,z Let us de ne the following encoding: A B C D E F G H The resulting state table is PS A B C D E F G H x=0 x=1 B,1 E,0 C,1 F,0 D,0 H,1 A,0 A,1 F,0 F,1 H,1 G,0 A,1 A,0 A,0 A,1 NS,z Input Let us try to reduce the number of states. P1 group 1 group 2 A,B,F,G C,D,E,H 0 1221 2111 1 2111 2111 B,F 45 23 G 1 1 C 5 5 D,E,H 121 121 P2 group 1 group 2 group 3 group 4 group 5 0 1 A 2 5 144 0 1 A 2 6 Solutions Manual - Introduction to Digital Design - Fe...
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