1. CS 140L Lecture 5 Professor CK Cheng 4/29/02

2. Asynchronous Counter D Q CLK D Q D Q There are n flip-flops. D FF is the delay of each flip-flop. When n * D FF > T, then we are in trouble.

3. Synchronous Counter D Q D Q D Q CLK BUFGP C(t+1) = C’(t) B(t+1) = B(t) + C(t) A(t+1) = A(t) + (B(t)C(t)) A B C A(t+1) B(t+1) C(t+1) 0 0 0 0 0 0 1 1 0 0 1 0 1 0 2 0 1 0 0 1 1 3 0 1 1 1 0 0 4 1 0 0 1 0 1 5 1 0 1 1 1 0 6 1 1 0 1 1 1 7 1 1 1 0 0 0 Check Chapter 8 for a synchronous counter using T F-Fs.

4. When comparing networks, there are two things to keep track of: Cost vs. performance. For example, the synchronous counter has better performance but higher costs due to the added gates. On the other hand, the asynchronous counter is easier to implement. As the length of the counter increases, the cost increases, since the the number of gates increases.

5. Johnson Counter D Q CLK CLR D Q D Q Q’ ABC 10 0 0 2 1 0 0 31 1 0 41 1 1 50 1 1 60 0 1 70 0 0 Time Steps A B C 1)Given n flip-flops, we have 2n states. Much less than previous counters. But Johnson is fast! 2)Only one output changes (low power). 3)Each output has n/f width (symmetrical). 4)Reset is important. (ie, we don’t want to start with 010 since if we do it ends up as 010- >101->010->101 etc.

6. Odd Length Walking – Ring Counter J K CLR Q Q’ J K Q J K Q ABC 0 0 11 0 0 2 1 1 0 30 1 1 40 0 1 50 0 0 61 0 0 71 1 0 Time Steps A B C J A K A A (t+1) 0 0 A(t) 0 1 0 1 0 1 1 1 A’(t) n JK F-Fs -> 2n-1 states The counter works itself back to the proper sequence.

7. Pseudo Random Sequencer n = 4, length = 15 D Q CLK D Q D Q D Q