The document provides an overview of digital counters, defining them as devices that store and count occurrences of events using flip-flops. It categorizes counters into asynchronous and synchronous types, further breaking them down into up, down, up-down, and decade counters while discussing their design principles and applications. Practical examples and design problems, such as constructing counts and counters for specific sequences, are also included.

1. Counters

2. What is a Counter?

3. Non Technical Definition
• A digital device which stores number of times
a particular event or process has occurred.
• This device counts the occurrence of events
with the help of multiple states
• Just like registers, we use basic storage
elements i.e. Flip-Flops to design counters.
• We can also display the stored count.

4. Technical Definition
• A register that goes through a prescribed
sequence of distinct states upon the
application of a sequence of input pulses
• Input pulses may be
– Clock pulses
– Originate from some other source
– May occur at regular or irregular interval of time

5. Binary Counter
• Counter that follows the binary number
sequence is called binary counter
• An n-bit binary counter consists of n flip-flops
and can count in binary from 0 through 2n
-1
• For example a counter which produces a
sequence of numbers like 00, 01, 10, 11 is a
binary counter.

6. Types of Counters
• Based upon type of clock, counters are of
following 2 types:
1. Asynchronous Counters.
2. Synchronous Counters.

7. Types of Counters
• Depending on the way in which the counting
progresses the Asynchronous and
Synchronous counters are classified as follows:
1. Up Counters
2. Down Counters
3. Up-Down Counters
4. Decade Counter.

8. Asynchronous Counters
A counter in which the flip-flops (FF) within the
counter do not change states at exactly the same
time because they do not have a common clock
pulse.
OR
A counter in which C input of some of the flip-flops are
triggered not by common pulse but rather by the
transitions that occur on other flip-flop outputs
e.g. Ripple counters

9. Synchronous Counters
A synchronous counter is one in which all the flip-
flops in the counter are clocked at the same time
by a common clock pulse
OR
In which the C inputs of all flip-flops receive common
pulse.

10. Designing Asynchronous Counters

11. 2 bit Asynchronous Binary UP Counter

12. State table

13. Timing Diagram

14. 3 bit Asynchronous Binary UP Counter

15. State Table

16. Timing Diagram

17. 4-bit Ripple Up Counter
What will be the state of counter on positive edge after 1111?

18. 4-bit Ripple Counter
• Design a 4-bit ripple
counter for downward
counting
Can you design an asynchronous Up-Down
Counter with Selection Input?

19. 4-bit Ripple Down Counter

20. Uses of Ripple Counter
• Propagation delay makes them less efficient
and slow.
• Used to measure
– Time, frequency, distance, speed
• Also used in
– Frequency division, direct counting, digital
computers

21. Designing Synchronous Counters

22. Synchronous 3-bit Up-Down Counter
For S=0
Count Upward
For S=1
Count Downward

23. Serial Counter
• A counter which is constructed with sequential
arrangement of flip-flops with the help of half
adders which provides information to each
stage about the state of the prior stages.
• If all the flip-flops are connected with same
clock , this type of arrangement is Synchronous
arrangement otherwise it is Asynchronous.

24. 4-Bit Synchronous Binary Counter

25. Serial Counter
EN
Q0(t)
Q1(t)
Q2(t)
Q3(t)
Q0(t+1)
Q1(t+1)
Q2(t+1)
Q3(t+1)
HA HA HA HA

26. Half Adder

27. Serial Counter

28. Serial Counter
Half Adders

29. Serial Counter
S0
S1
S2
S3
C1
C2
C3
C4

30. Serial Counter
If EN = 0, Hold Data
If EN = 1, Increment by 1

31. How Serial Counter Works?
0
1
0
0
Value at time t = 0010
What will be the value at time t+1
1

32. How Serial Counter Works?
0
1
0
0
1
Qi outputs coming to
XORs and ANDs

33. How Serial Counter Works?
0
1
0
0
1
1
0

34. How Serial Counter Works?
0
1
0
0
1
1
0
1
0

35. How Serial Counter Works?
0
1
0
0
1
1
0
1
0
0
0

36. How Serial Counter Works?
0
1
0
0
1
1
0
1
0
0
0
0
0

37. How Serial Counter Works?
0
1
0
0
1
1
0
1
0
0
0
0
0
Value of this AND depends
On three ANDs in previous
Levels of gating

38. How Serial Counter Works?
0
1
0
0
This data will be
available at next tick
1
1
0
1
0
0
0
0
0

39. How Serial Counter Works?
1
1
1
0
0

40. Parallel Counter
Clock

41. How Parallel Counter works?
Clock
Value at time t = 0010
What will be the value at time t+1
0
1
0
0
1

42. How Parallel Counter works?
Clock
0
1
0
0
1

43. How Parallel Counter works?
Clock
0
1
0
0
1
0
0
0
0
This signal 0 is coming from Q0
1

44. How Parallel Counter works?
Clock
0
1
0
0
1
0
0
0
0
All the ANDs which got 0
Gave output 0
1

45. How Parallel Counter works?
Clock
1
0
0
1
0
X XOR 1 = X’
X XOR 0 = X
1

46. How Parallel Counter works?
Clock
1
0
0
1
0
This data will be available
On counter output at time t+1
1

47. How Parallel Counter works?
Clock
1
0
0
1
0
Counter at time t+1
1

48. Serial VS Parallel Counter
Gate delay being accumulated in Serial Counter as last AND is at level 4 of gating.
For example, going from state 1111 to state 0000.
Clock

49. Serial VS Parallel Counter
Output of 4th
AND gate depends on the outputs of all previous AND gates.
i.e. Delay of four AND Gates being accumulated.
Clock

50. Practice Problems
1. Arbitrary Count Sequence: Design a
synchronous counter which follows sequence
given below:
0, 2, 4, 6, 8, 0, 2,…
2. BCD Counter: Design a BCD synchronous counter
which follows the sequence given below:
0,1,2,3,4,5,6,7,8,9,0,1,2,…

51. Practice Problems
3. Modulo-7 Counter: Which follows the
sequence 0,1,2,3,4,5,6,0,1,2,…
4. Digital Watch
For your convenience consider we have 64
seconds in one minute, 64 minutes in one
hour and total 32 hours in a day.

52. Practice Problems
5. Automatic Parking Control
Take CarIn and CarOut signals from sensors at Entry
and Exit Gates respectively. Parking area has total
capacity of 32 cars, when total count of cars in the
plaza reaches 32 lock the Entry Door otherwise the
door will remain unlocked.
6. Counter with Parallel Load
Register composed of D Flip-Flops which loads the
data if Load = 1 otherwise behaves like a binary
counter.

53. Practice Problems
7. Counter composed of D Flip-Flops which
takes X and Y selection inputs and performs
following operations:
X Y Operation
0 0 Count
0 1 Shift Right
1 0 Shift Left
1 1 Parallel Load