Unformatted text preview: nical version of this sequential network is presented in Figure 8.5 on page 125. The state diagram for this system is presented in Figure 8.6. State S1 represents a 1 followed by a EVEN block of zeros, and state S5 indicates that the system received the required sequence. The corresponding state table is: Input PS x = 0 x = 1 S0 S0 S1 0 S1 S2 S3 0 S1 0 S2 S1 S3 S2 S4 0 S4 S5 S4 0 S5 S4 S1 1 NS outputz
Exercise 8.7 y1 0 1 0 0 0 1 y1 y2 1 0  y1 Y0 : 1001 y1 Solutions Manual  Introduction to Digital Design  February 22, 1999 125 Combinational Network Y2 Y1 Y0 y2 cells y1 y0 Comb. Network z1 z0 y1 y0 y2 y0’
y2’ y1’ y0 y2’ y2 y1’ y1 y0’ y0 CK y1 y0’ z1 z0 Figure 8.5: Pattern generator of Exercise 8.6 We use the state code i in binary for the state Si . The PS is represented by the 3bit vector y2 y1 y0 and the NS by the vector Y2 Y1 Y0 . The output switching expression is: z = y2 y0
The Kmaps for the next state bits are shown next. 1 0 S0/0 1 S1/0 0,1 S2/0 0 1 S3/0 0 S1  block of zeros of EVEN length S5  block of zeros of ODD length (after correct prefix) 1 1 0 S4/0 0 S5/1 Figure 8.6: State diagram for Exercise 8.7 126 y0 0 1 1 0 0 1 0 0 0 1 y1 Solutions Manual  Introduction to Digital Design  February 22, 1999 y0 0 y2 0 0 0 0 0 1 0 0 1 1 0 y1 0 y2 0 0 1 0 1 0 0 1 1 y0 0 0 y1 1 y2 1 x x x Y2: Y1 : Y0: The switching expression for Y2 ,Y1 , and Y0 are:
0 Y2 = y2 y0 + x0 y2 + xy1y0 00 0 Y1 = y2 y1 y0 + x0 y2y0 00 0 0 0 Y0 = xy2y1 + xy1y0 + y1 y0 + x0 y2 y0 The corresponding sequential network is shown in Figure 8.7.
y2 y0’ x’ y2 x y1 y0 y2’ y1’ y0 x’ y2’ y0 x y2’ y1’ x y1’ y0 y1 y0’ x’ y2 y0’
y2 Y2 x x’ Y1
y1 y0 z y0’ CK Y0 y2 y1 y2’ y1’ Figure 8.7: Network for Exercise 8.7 Solutions Manual  Introduction to Digital Design  February 22, 1999 127 We need a 3bit vector to represent the six states and a 2bit vector to represent the output. Let us de ne the following encoding: y2y1 y0 State 000 A z1 z0 001 B 00 a C...
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 Winter '09
 Ercegovac,M.D.
 Nondeterministic finite state machine, State transition table

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