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Unformatted text preview: tion of a JK ip op is PS 0 1 NS 01 0 11 0 JK Input the inputs J1 ; K1 ; J2 , and K2 to the JK ip ops are Q 2 Q1 x = 0 x = 1
00 01 10 0,00,1 1,0 PS J2 K2 ; J1 K1 0,11,1 0,0 Switching expressions for these ip op inputs are J2 = Q1 x K2 = x0
An expression for the output is J1 = Q02 x K1 = 1 z = Q2 x0 The sequential network is shown in Figure 8.26.
Q1 J CK 1 1 CK x K Q’ Q J CK 2 K x’ Q’ Q Q2 z Figure 8.26: Network for Exercise 8.23 Since the output at time t depends on the inputs at time t , 3; t , 2; t , 1, it is necessary to store these in the state register. That is, the register consists of three ip ops such that
Exercise 8.24 Q2 t = xt , 3 Q1 t = xt , 2 Q0 t = xt , 1 148 Solutions Manual  Introduction to Digital Design  February 22, 1999 Consequently, the state description is Q2 t + 1 Q1 t + 1 Q0 t z = = = = Q1 t Q0 t xt xt , 3 xt , 2 xt , 1 xt = Q2 Q1 Q0 x D2 = Q1 D1 = Q0 D0 = x If we use D ip ops, we get The sequential network is shown in Figure 8.27.
Z Q0 X
D Q D Q Q1
D Q FF0
Q’ FF1
Q’ FF2
Q’ CK Figure 8.27: Network for Exercise 8.24
Exercise 8.25 We have to store the last input to be able to recognize the sequence 11; therefore, we need: S0 : xt , 1 = 0 S1 : xt , 1 = 1
The state table is PS NS,z Coding S0 as 0 and S1 as 1, the resulting state table is Input PS Q x=0 x=1 0 0,0 1,0 1 0,0 1,1 NS,z S0 S1 x=0 x=1 S0 ; 0 S1; 0 S0 ; 0 S1; 1 Input Solutions Manual  Introduction to Digital Design  February 22, 1999 149 We only need one JK ip op. Since its excitation function is PS NS 01 1 0 11 1 0 JK the inputs are J=x K = x0
The output is described by z = Qx The sequential network is shown in Figure 8.28. Z X CK J CK K Q’ Q Figure 8.28: Network for Exercise 8.25
Exercise 8.26 The state corresponds to the count. That is, st + 1 = st + 1 mod 3
Using a radix2 representation for the count we get the following state table PS Input Q 2 Q1 x = 0 x = 1 00 00 01 01 01 10 10 10 00 NS Since the excitation function of a SR ip op is PS...
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This note was uploaded on 03/26/2010 for the course CS 187154200 taught by Professor Ercegovac,m.d. during the Winter '09 term at UCLA.
 Winter '09
 Ercegovac,M.D.

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