1. A presentation on Counters (second)
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2. Review Counters: Two principal categories
Counters are divided in two categories, these are:
Asynchronous (Ripple) Counters - the first flip-flop is clocked by the external clock pulse, and then each successive flip-flop is clocked by the Q or Q' output of the previous flip-flop.
Synchronous Counters - all memory elements are simultaneously triggered by the same clock.

3. Two-bit asynchronous counter
A two-bit asynchronous counter is shown on the left.
It uses two J-K flip flops.

4. Three-bit asynchronous counter

5. A Decade Counter (asynchronous counter)

6. SYNCHRONOUS COUNTER

7. Synchronous counters
In synchronous counters, the clock inputs of all the flip-flops are connected together and are triggered by the input pulses.  
Thus, all the flip-flops change state simultaneously (in parallel).  
The circuit below is a 3-bit synchronous counter.  

8. 3-bit Synchronous counter

9. Synchronous counters The J and K inputs of FF0 are connected to HIGH.
FF1 has its J and K inputs connected to the output of FF0, and the J and K inputs of FF2 are connected to the output of an AND gate that is fed by the outputs of FF0 and FF1.

10. Synchronous counter

11. Synchronous counter
Pay attention to what happens after the 3rd clock pulse.  
Both outputs of FF0 and FF1 are HIGH.  
The positive edge of the 4th clock pulse will cause FF2 to change its state due to the AND gate.
Q0: FF0
Q1: FF1
Q2: FF2

12. Synchronous counter
The count sequence for the 3-bit counter is shown on the right.

13. Synchronous counter
The most important advantage of synchronous counters is that there is no cumulative time delay because all flip-flops are triggered in parallel.  
Thus, the maximum operating frequency for this counter will be significantly higher than for the corresponding ripple counter.

14. Synchronous Decade Counters
Similar to an asynchronous decade counter, a synchronous decade counter counts from 0 to 9 and then recycles to 0 again.  
This is done by forcing the 1010 state back to the 0000 state.  
This so called truncated sequence can be constructed by the following circuit.

15. Synchronous Decade Counters

16. Synchronous Decade Counters
From the sequence on the left, we notice that: Q0 toggles on each clock pulse.

17. Synchronous Decade Counters
Q1 changes on the next clock pulse each time Q0=1 and Q3=0.

18. Synchronous Decade Counters
Q2 changes on the next clock pulse each time Q0=Q1=1.
Q3 changes on the next clock pulse each time Q0=1, Q1=1 and Q2=1 (count 7), or when Q0=1 and Q3=1 (count 9).

19. Synchronous Up-Down Counters
A circuit of a 3-bit synchronous up-down counter and a table of its sequence are shown below.  
Similar to an asynchronous up-down counter, a synchronous up-down counter also has an up-down control input.  
It is used to control the direction of the counter through a certain sequence.

20. Synchronous Up-Down Counters

21. Synchronous Up-Down Counters
An examination of the sequence table shows: for both the UP and DOWN sequences, Q0 toggles on each clock pulse.

22. Synchronous Up-Down Counters
for the UP sequence, Q1 changes state on the next clock pulse when Q0=1.

23. Synchronous Up-Down Counters
for the DOWN sequence, Q1 changes state on the next clock pulse when Q0=0.

24. Synchronous Up-Down Counters
for the UP sequence, Q2 changes state on the next clock pulse when Q0=Q1=1.
for the DOWN sequence, Q2 changes state on the next clock pulse when Q0=Q1=0.

25. Applications Digital counters are very useful in many applications.
They can be easily found in digital clocks and parallel-to-serial data conversion (multiplexing).

26. Applications
A group of bits appearing simultaneously on parallel lines is called parallel data.  
A group of bits appearing on a single line in a time sequence is called serial data.  
Parallel-to-serial conversion is normally accomplished by the use of a counter to provide a binary sequence for the data-select inputs of a multiplexer, as illustrated in the circuit below.

27. Applications

28. Applications
The Q outputs of the modulus-8 counter are connected to the data-select inputs of an eight-bit multiplexer.  
The first byte (eight-bit group) of parallel data is applied to the multiplexer inputs.  
As the counter goes through a binary sequence from 0 to 7, each bit beginning with D0, is sequentially selected and passed through the multiplexer to the output line.

29. Applications
After eight clock pulses, the data byte has been converted to a serial format and sent out on the transmission line.  
Then, the counter recycles back to 0 and converts another parallel byte sequentially again by the same process.

30. Merry Christmas, Happy New Year and Happy 3 Kings Day!
STUDY!!!