1. Counter with Unused
States

2. Counters with Unused States
n
• A circuit with n flip-flops has 2 states
• There are occasions when a sequential
circuit uses fewer than there maximum
possible number of states. States that
are not used in specifying the sequential
circuit are not listed in the stable table.

3. Counter with Unused States

4. Unused States
• For example, here is a state table and diagram for
a counter that repeatedly counts 000, 001, 010,
100, 101, 110.
Present State Next State
Q2 Q1 Q0 Q2 Q1 Q0
0 0 0 0 0 1
0 0 1 0 1 0
0 1 0 0 1 1
1 0 0 1 0 0
1 0 1 1 0 1
1 1 0 0 0 0
0 1 1 ? ? ?
1 1 1 ? ? ?

5. Unused States
• Unused states may be treated as don’t care or
assigned specific next state
Present State Next State Present State Next State
Q2 Q1 Q0 Q2 Q1 Q0 Q2 Q1 Q0 Q2 Q1 Q0
0 0 0 0 0 1 0 0 0 0 0 1
0 0 1 0 1 0 0 0 1 0 1 0
0 1 0 0 1 1 0 1 0 0 1 1
1 0 0 1 0 0 1 0 0 1 0 0
1 0 1 1 0 1 1 0 1 1 0 1
1 1 0 0 0 0 1 1 0 0 0 0
0 1 1 X X X 0 1 1 1 0 0
1 1 1 X X X
1 1 1 0 0 0

6. Ring Counters
• A ring counter is a type of counter composed of a
circular shift register with only one flip-flop being set
at any particular time.
• If the output of a shift register is fed back to the
input. a ring counter results
• Two types of Ring Counters
• Straight Ring Counter
• Switch-Tail Ring Counter or
Twisted Ring Counter

7. Straight Ring Counter
• or Overbeck counter connects the output of the last
shift register to the first shift register input and
circulates a single one (or zero) bit around the ring.

8. Straight Ring Counter
• Loading binary 1000 into the ring counter prior to
shifting yields a viewable pattern. The data pattern
for a single stage repeats every four clock pulses in
our 4-stage example

9. Straight Ring Counter
• The waveforms for all four stages look the
same, except for the one clock time delay from
one stage to the next. See figure below.
Capable of generating different timing signals

10. Twisted Ring Counter
(Johnson Counter)
• The number of state is (or can be) doubled by choosing
this type of circuit.
• Like a Straight ring counter a Johnson counter is a
shift register fed back on its' self.
• If the complement output of a ring counter is fed back
to the input instead of the true output, a Johnson
counter results.

11. Johnson Counter

12. Johnson Counter
• This "reversed" feedback connection has a profound
effect upon the behavior of the otherwise similar
circuits. Circulating a single 1 around a ring counter
divides the input clock by a factor equal to the
number of stages. Whereas, a Johnson counter
divides by a factor equal to twice the number of
stages. For example, a 4-stage ring counter divides by
4. A 4-stage Johnson counter divides by 8.

13. Johnson Counter
• Determine the output pulses for this counter circuit,
known as a Johnson counter, assuming that all Q
outputs begin in the low state:

14. Johnson Counter
Ans.

15. Johnson Counter
• The above waveforms illustrates that multi-phase
square waves are generated by a Johnson counter.
The 4-stage unit above generates four overlapping
phases of 50% duty cycle.

16. Ring Counter