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Lecture 24 - ECE52 Spring 11 Lecture 24(reordered from past...

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1 ECE52 Spring 11 Lecture 24 3/16/11 (reordered from past years to get to counters faster)
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Sequential building blocks Registers Counters 2
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3 Counters! Ubiquitous inside computers and other digital systems counting occurrences of events generating timing intervals (“initiate an event 7 clockcycles in the future” requires a counter) count elapsed time between events loop iterations
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4 Using chapter 8 techniques… Counter as a FSM – a particularly simple FSM! Consider modulo-8 counter – cycles through 0- 1-2-3-4-5-6-7-0-1-… every time the input w is active. w 0 = w 1 = w 0 = w 1 = w 0 = w 1 = w 0 = w 1 = w 0 = w 1 = w 0 = w 1 = w 0 = w 1 = w 0 = w 1 = A/0 B/1 C/2 D/3 E/4 F/5 G/6 H/7
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5 State table for mod-8 counter Present Next state Output state w = 0 w = 1 A A B 0 B B C 1 C C D 2 D D E 3 E E F 4 F F G 5 G G H 6 H H A 7
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6 Obvious state assignment for counter Present Next state state w = 0 w = 1 Count y 2 y 1 y 0 Y 2 Y 1 Y 0 Y 2 Y 1 Y 0 z 2 z 1 z 0 A 000 000 001 000 B 001 001 010 001 C 010 010 011 010 D 011 011 100 011 E 100 100 101 100 F 101 101 110 101 G 110 110 111 110 H 111 111 000 111 intiutively make state flip flop values be the output signals directly!
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7 Why flip-flop choice matters: Consider D-flip flop implementation 00 01 11 10 00 01 1 0 1 1 1 0 0 0 0 1 0 0 0 1 1 1 11 10 y 1 y 0 wy 2 00 01 11 10 00 01 0 0 0 1 1 1 1 0 1 0 1 0 0 1 1 0 11 10 y 1 y 0 wy 2 00 01 11 10 00 01 0 1 1 0 1 0 1 0 1 0 0 0 1 1 0 1 11 10 y 1 y 0 wy 2 Y 2 wy 2 y 0 y 2 y 1 y 2 w + + + y 0 y 1 y 2 = Y 0 wy 0 wy 0 + = Y 1 wy 1 y 1 y 0 wy 0 y 1 + + =
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8 D Q Q D Q Q Clock y 0 w y 1 y 2 Y 0 Y 1 Y 2 Resetn D Q Q D flip-flop implementation of mod-8 counter
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9 Now consider J-K implementation Present Flip-flop inputs state w = 0 w = 1 Count y 2 y 1 y 0 Y 2 Y 1 Y 0 J 2 K 2 J 1 K 1 J 0 K 0 Y 2 Y 1 Y 0 J 2 K 2 J 1 K 1 J 0 K 0 z 2 z 1 z 0 A 000 000 0d 0d 0d 001 0d 0d 1d 000 B 001 001 0d 0d d0 010 0d 1d d1 001 C 010 010 0d d0 0d 011 0d d0 1d 010 D 011 011 0d d0 d0 100 1d d1 d1 011 E 100 100 d0 0d 0d 101 d0 0d 1d 100 F 101 101 d0 0d d0 110 d0 1d d1 101 G 110 110 d0 d0 0d 111 d0 d0 1d 110 H 111 111 d0 d0 d0 000 d1 d1 d1 111
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10 K-maps for JK implementation 00 01 11 10 00 01 d 0 d d d 0 0 0 d 1 d d d 1 1 1 11 10 y
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