Design Example: Counters. Design Example: Counters. 3-Bit Binary Counter. 3-Bit Binary Counter. Other useful counters:

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1 Design Eample: ers er: a sequential circuit that repeats a specified sequence of output upon clock pulses. A,B,C,, Z. G, O, T, E, R, P, S,!.,,,,,,,7. 7,,,,,,,.,,,,,,,,,,,. Binary counter: follows the binary sequence. -bit (up) binary counter:,,,. -bit down binary counter: 7,,,,,,, Design Eample: ers Other useful counters: Decimal counter (e.g. BCD counter),,,,,,,, Modulo-k counter Modulo- counter:,,,,,,,, M-to-N counter -to-8 counter:,,,,7,8,,, Ripple counter Ring counter and ohnson counter -Bit Binary er -Bit Binary er (t) (t+) T current state net state flip-flop inputs A B C A B C TA TB TC Flip-flop input functions TA = BC TB = C TC = T A T B T C Figure. gives a -bit binary counter. When =C, =B, =A, delete, set enable bit to be constant, it becomes this -bit counter.

2 Binary er with Flip-Flops E A -Down Binary er E A (t) (t+) when E = and goes from to : A A A A A A A A A A Eercise: Verify that the circuit is a binary counter that counts down from to, and then back to again. A A A A A A A A Summary Binary er with Parallel Sequential circuit design eample Shift registers Basic counters Net time Binary counter with parallel Ripple counter ohnson counter Net Monday: Eam IV PLD, Chapter, 7., 7. Discussion on Wednesday s class control signals, modes: ( i =D i ) = (up) =, = No change =, = (change, or count, happens only at positive edge of the clock pulse.) Carry Out: if and only if the counter is in count mode with content. Read Figure. for the detailed implementation. D D

3 9 7 8 modulo- Modulo-7 er modulo-7 (when to ) D D modulo- -To-8 er D D -to-8 (when and what to ) Design Eample Eam IV 8-bit counter with two ers D D D D 7 PLD Timing diagram for basic latch/flip-flop Sequential circuit analysis Sequential circuit design Registers and counters

4 Ripple er Synchronous counter: the signal of all flipflops are from the common clock. Ripple counter: the of some flip-flops are from other flip-flops (and through logic gates). Ripple counter is asynchronous Binary ripple (up) counter (read Figure.) Binary ripple down counter Where the signal comes from? (By default, flip-flop is positive edge triggered.) BCD Ripple er Verify the following circuit is a BCD Ripple counter triggered by negative edge. 8 BCD Ripple er Verify the following circuit is a BCD Ripple counter triggered by negative edge. Ring er Ring counter: a circular shift register (with k flipflops) that at any time, only one flip-flop is set (having value ) and all others are cleared (with value ). It is used to generate k (periodic) timing signals. Eample: see Figure.7 for circuit. A D 8 C B

5 Ring er as er + Decoder ohnson er To generate (periodic) timing signals, we need a -bit ring counter, or a -bit counter and a decoder. -bit count decoder D C B A ohnson counter: a k-bit circular shift register with the complement of the last flip-flop connected to the input of the first flip-flop, and k decoding gates. It is used to generate k (periodic) timing signals. AND gates for decoding S S S D D D ohnson er S S S D D D states AND gate for output S S S T T T T T T AND gates for decoding S S S T = S S T = S S T = S S T = S S T = S S T = S S