hw8_solutions

# hw8_solutions - Chapter 6 6.1 w3 w2 w1 w0 w1 w2 y0 y1 y2 y3...

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Unformatted text preview: Chapter 6 6 .1 . w3 w2 w1 w0 w1 w2 y0 y1 y2 y3 Homework 8 Solutions f y4 y5 y6 1 6 .2 . En y7 w3 w2 w1 w0 w1 w2 y0 y1 y2 y3 f y4 6 .4 . 6 .3 . 6 .4 . 6 .5 . w 1 w 2 wy 5 3 y6 000 y 1 En 0 1 7 0 010 011 100 101 w1 w2 w3 110 10 10 10 001 w0 w1 w0 123 011 w2 01 00 00 w3 01 00 11 01 11 00 01 11 11 100 101 The function f can be express1w as 0 ed 1 2 111 w3 f w1 f 0 1 1 0 0 0 1 0 f 1 1 1 0 f1 1 10 00 01 00 1 0 1 1 w2 w3 w2 + w3 w1 f 0 1 w2 + w3 w1 w2 w3 w1 f 0 1 w2 + w3 w2 w3 f w1 f = w1 w2 w 3 + w 1 w2 w 3 + w 1 w2 w3 + w1 w2 w 3 f Expansion in terms of w1 produces w1 f = w 1 (w2 + w3 ) + w1 (w2 w 3 ) w2 w3 The corresponding circuit is f 6-1 w1 w2 w 6.5. The function f can be ex3 ressed as p f f = w1 w2 w 3 + w 1 w2 w 3 + w 1 w2 w3 + w1 w2 w 3 Expansion in terms of w1 produces f = w 1 (w2 + w3 ) + w1 (w2 w 3 ) 6.6. The function f can be expressed as The corresponding circuit is f = w1 w2 w3 + w1 w2 w3 + w1 w2 w 3 + w1 w2 w3 Expansion in terms of w2 produces w2 w1 f = w 2 (w 3 ) + w2 (w1 ) wi The corresponding circuit 3 s f w2 w3 f w 6.6. The function f can be expressed as 1 f = w1 w2 w3 + w1 w2 w3 + w1 w2 w 3 + w1 w2 w3 Expansion in terms of w2 produces 6-2 f = w 2 (w 3 ) + w2 (w1 ) The corresponding circuit is w2 w3 f w1 6-2 ECE 152A Summer 2011 H.O. #23 6 .3 2 . 2-to-4 decoder VDD a0 a1 d3 d2 d1 d0 8.26. The state diagram is Present Next state state w=0 w=1 A B C D E F G H H A B C D E F G Count C D E F G H A B 0 1 2 3 4 5 6 7 The state-assigned table is Present state y2 y1 y0 A B C D E F G H 000 001 010 011 100 101 110 111 Next state w=0 w=1 Y2 Y1 Y0 Y2 Y1 Y0 111 000 001 010 011 100 101 110 6-15 010 011 100 101 110 111 000 001 Output z2 z1 z0 000 001 010 011 100 101 110 111 The next-state expressions (inputs to D ﬂip-ﬂops) are D2 D1 = Y2 = Y1 = w y 2 y1 + w y 2 y1 + w y 2 y 1 + w y 2 y0 + y 2 y 1 y 0 w = w y 1 + y 1 y 0 + w y 1 y0 D0 = Y0 = y 0 w + y0 w The outputs are: z2 = y2 , z1 = y1 , and z0 = y0 . 8-16 ...
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