CSM51Asolution_chapter8

33 network for exercise 829 the modulo 5 counter

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Unformatted text preview: 011 100 PS 0000-1 x=0 00-0 -1 0- Input 1-0 1-0 10010-1 x=1 01-1 -0 0- J2 K2 J1 K1 J0 K0 xQ1 Q00 1 0-1 0-1 0- Using K-maps we get the following switching expressions: J2 K2 J1 K1 J0 K0 The output expression is: = = = = = = xQ0 xQ00 + x0Q0 x0 x The sequential network is shown in Figure 8.33 x Q1 Q0’ x x’ "1" z = x0 Q2 + xQ1 Q0 Q2 J CK 2 Q x’ Q2’ z x Q0 K Q’ x Q1 J Q0 x Q0’ x’ Q0 x’ CK x Q CK 1 K Q’ Q1’ Q0 J CK 0 K Q Q’ Q0’ Figure 8.33: Network for Exercise 8.29 The modulo-5 counter presented in Example 8.8 was implemented using T-type ip- op. For this problem we need to synthesize di erent functions for D-type ip- ops. The transition table, though, is exactly the same. Exercise 8.30 Solutions Manual - Introduction to Digital Design - February 22, 1999 157 Q2Q1 Q0 000 001 010 011 100 PS Input x=0 x=1 000 001 001 010 010 011 011 100 100 000 NS Since the D-type ip- ops has as inputs the bits of the next state shown in the transition table, the K-maps are: Q0 0 1 0 0 0 0 0 1 0 Q -2 0 0 0 0 0 Q0 0 1 1 0 1 Q -2 1 0 0 0 1 Q0 1 0 1 0 0 Q -2 1 x D2 : x D1 : x D0 : Q1 Q1 Q1 The inputs of the D-type ip- ops are: D2 = xQ1Q0 + x0 Q2 D1 = xQ01Q0 + Q1 Q00 + x0 Q1 D0 = xQ02Q00 + x0 Q0 The gate network for the sequential system is presented in Figure 8.34. Comparing Figure 8.34 with Figure 8.28 of the text we can easily see that this implementation uses more gates than the one done with T-type ip- ops. To implement Example 8.9 using JK ip- ops we use the following state transition table and output, that already includes the appropriate input functions for the ip- ops: Exercise 8.31 Q1 Q0 00 01 10 11 PS 01 01,0 00,0 11,0 10,0 Input 10 10,1 11,1 10,0 00,0 NS, z 11 10,0 11,0 00,1 11,1 01 0-101 -01-0-1 J1 K1 J0 K0 Input 10 1-010 -00-1-1 11 1-010 -10-0-0 The Kmaps for the combinational circuit that activates the JK inputs of the ip- ops are: 158 Solutions Manual - Introduction to Digital Design - February 22, 1999 x Q1 Q0 x’ Q2 D2 D Q Q2 CK Q2’ Q’ x Q1’ Q0 Q1 Q0’ x’ Q1 D1 D Q Q1 CK Q1’ Q’ x Q2’ Q0...
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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.

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