1. Principles & Applications
Digital Electronics
Principles & Applications
Seventh Edition
Roger L. Tokheim
Chapter 8
Counters
©2008 The McGraw-Hill Companies, Inc. All rights reserved.

2. INTRODUCTION Overview of Counters Characteristics of Counters
Ripple Up Counter
Ripple Counter with Waveforms
Ripple Down Counter
Self-stopping Counter
Frequency Division using Counters
Using Counter ICs
Magnitude Comparators
Troubleshooting Hints

3. Overview of Counters Counter-by definition One input (clock)
Outputs follow defined sequence
Common tasks of counter
Count up or down
Increment or decrement count
Sequence events
Divide frequency
Address memory
As temporary memory

4. QUIZ
1. A digital counter has a single clock input with many outputs and the counter follows defined sequence such as 000, 001, 010, 011, 100, 101, 110, 111, 000, etc. (True or False)
True
Several common tasks of a counter are to count up or down, divide frequency, or as temporary memory. (True or False)
True

5. Characteristics of Counters
Number of bits (4-bit, 8-bit, etc.)
Maximum count
4 bit = 24 = 0000 to 1111 in binary
8 bit = 28 = to in binary
Modulus of counter-number of states
Decade counter
4-bit
8-bit
Up or down counter
Asynchronous or synchronous counter
Presettable counter
Self-stopping counter

6. QUIZ 1. A 4-bit counter will count from binary 0000 to __________.
1111
2. The modulus of a counter is the number of states it will cycle through such as a decade counter has a modulus of __________. 10
3. Counters can be designed to count up or downward or devised to be self-stopping. (True or False)
True
4. A 4-bit counter would have modulus of 4 (mod-4 counter) because it is constructed using four flip-flops. (True or False)
False

7. Ripple Counter
Binary Output
Clock Input
Pulse 5
Pulse 6
Pulse 8
Pulse 4
Pulse 7
Pulse 1
Pulse 2
Pulse 3
This 4-bit counter has 16 states and
will count from binary 0000 through 1111
and then reset back to 0000.
The counter has a modulus of 16.
On the next clock pulse (8) all FFs
will toggle because each will receive
a H-to-L pulse- one after another.
Watch the count ripple thru the counter.
All J-K flip-flops
in the
TOGGLE MODE
PS and CLR inputs
are
INACTIVE

8. Ripple Counter With Waveforms
Binary Output
Clock Input
Pulse 5
Pulse 4
Pulse 2
Pulse 3
Pulse 1
Clock input
1s output
2s output
4s output
FFs triggered on
H-to-L pulse.
CLK toggles 1s FF.
1s FF toggles 2s FF.
2s FF toggles 4s FF.

9. QUIZ
Q#1- After pulse 1 the output of the mod-16
counter will be binary ___.
Q#2- After pulse 2 the output of the mod-16
counter will be binary ___.
Q#3- After pulse 8 the output of the mod-16
counter will be binary ___.
Q#4- After pulse 15 the output of the mod-16
counter will be binary ___.
Pulse 15
Pulse 8
Pulse 2
Pulse 1
Input Pulses

10. Decade Counter All J & K inputs = 1 All PR inputs = 1 0 0 0 1 0 0 0 0
Initial count at 0111
Binary Output
Clock Input
Pulse 8
Pulse 2
Pulse 1
Pulse 4
Pulse 3
Pulse 7
Pulse 6
Pulse 5
To clear input
of each FF
Short negative pulse
All J & K inputs = 1
All PR inputs = 1
Count is at 1001.
Next clock pulse will increment counter for a
short time to 1010 which will activate the NAND gate
and reset the counter to 0000.
To change mod-16 counter to decade counter:
Reset count to 0000 after 1001 (9) count.
When count hits 1010 reset to 0000.
See added 2-input NAND gate that clears all
JK FFs to 0 when count hits 1010.

11. QUIZ 0 1 1 0 Q#1- This is a ___ (mod-10, mod-16) up counter.
Q#2- This circuit can be described as a ___ (decade, 4-bit)
up counter.
Q#3- The ___ gate generates a very short LOW pulse when the
count reaches 1010 and resets to counter to 0000.
Q#4- After 0110, the counting sequence would be 0111, 1000,
1001, 1010, 1011, 1100, 1101, 1110, 1111, 0000, etc. (T or F)
ANS: mod-10
ANS: decade
ANS: NAND
ANS: False
Input pulses
To clear input
of each FF

12. Down Counter
Initial count
set at
binary 111
0 1 1
0 1 0
1 0 0
1 0 1
1 1 0
1 1 1
Pulse 2
Pulse 5
Pulse 4
Pulse 1
Pulse 3
Changes from Ripple Up Counter are
wiring from Q’ outputs (instead of Q outputs)
to the CLK input of the next FF.

13. QUIZ 1 1 1 Q#1- This circuit can be described as a 3-bit ripple ___
(down-counter, up-counter).
Q#2- This circuit is a self-stopping 3-bit ripple down counter.
(T or F)
Q#3- The counting sequence of this circuit is 111, 110, 101,
100, 011, 010, 001, 000, 111, 110, 101, 100, etc. (T or F)
ANS: down-counter
ANS: False
ANS: True
Input pulses

14. Self-Stopping Down Counter
Watch count on
Pulse 8.
The count remained
at binary 000.
0 1 1
0 1 0
0 0 0
1 0 1
0 0 1
1 0 0
1 1 0
1 1 1
Pulse 8
Pulse 1
Pulse 7
Pulse 2
Pulse 6
Pulse 5
Pulse 4
Pulse 3
This is a 3-bit down counter.
The 1s FF is in TOGGLE mode when counting (J & K = 1).
The 1s FF switches to HOLD mode when the J and K inputs are forced LOW by the OR gate
when the count decrements to The count stops at 000.

15. QUIZ 1 1 1 Q#1- This circuit could be described as a 3-bit ___
(decade, self-stopping) ripple counter.
Q#2- The 3-input OR gate generates a ___ (HIGH, LOW)
when the count decreases to 000 which stops the count at 000.
Q#3- With the count at 111, the OR gate outputs a HIGH
which places the left FF in the toggle mode. (T or F)
ANS: self-stopping
ANS: LOW
ANS: True
Input pulses

16. Counter Used for Frequency Division
 4
200 Hz
 8
400 Hz
100 Hz
50 Hz
 2
 16
Clock Input
800 Hz

17. QUIZ Frequency? Frequency? Frequency? Frequency? Frequency? 3200 Hz
Q#1- What is the output frequency
from the 1s J-K flip-flop with an
input frequency of 3200 Hz?
Q#2- What is the output frequency
from the 2s J-K flip-flop with an
input frequency of 3200 Hz?
Q#3- What is the output frequency
from the 4s J-K flip-flop with an
input frequency of 3200 Hz?
Q#4- What is the output frequency
from the 8s J-K flip-flop with an
input frequency of 3200 Hz?
Q#5- The 8s output from the 4-bit
counter is referred to as the ___
(divide-by-4, divide-by-16) output.
ANS: 1600
ANS: 800
ANS: 400
ANS: 200
ANS: divide-by-16
Frequency?
Frequency?
Frequency?
Frequency?
Frequency?
Clock Input
3200 Hz

18. Using the 7493 Counter IC Counters are available in IC form.
Either ripple (7493 IC) or synchronous (74192 IC) counters are available.
? Hz
400 Hz
100 Hz
? Hz
? Hz
800 Hz
1600 Hz
7493 Counter IC
wired as a 4-bit
binary counter

19. Magnitude Comparator
A magnitude comparator is a combinational logic device that compares the value of two binary numbers and responds with one of three outputs (A=B or A>B or A<B).
74HC85
Magnitude
Comparator
A = B
A < B
A > B
A(0)
A(1)
A(2)
A(3)
B(0)
B(1)
B(2)
B(3)
Input binary 0111
Input binary 1111
Input binary 0001
HIGH
HIGH
Input binary 0110
Input binary 0111
Input binary 1100
HIGH

20. QUIZ Q#1- The 74HC85 Comparator IC compares two 4-bit ___
(binary, decimal) numbers (A and B) and generates one of three
outputs including (1) A = B, (2) A > B, or (3) A < B.
Q#2- Which output of the comparator IC will be activated
with these two 4-bit binary numbers as inputs?
Q#3- Which output of the comparator IC will be activated
with these two 4-bit binary numbers as inputs?
Q#4- Which output of the comparator IC will be activated
with these two 4-bit binary numbers as inputs?
ANS: binary
ANS: A = B
ANS: A < B
ANS: A > B
74HC85
Magnitude
Comparator
A = B
A < B
A > B
A(0)
A(1)
A(2)
A(3)
B(0)
B(1)
B(2)
B(3)
0101
0101
1101 ?
0101
1011
1010

21. Simple Troubleshooting Hints
Feel top of IC to determine if it is hot
Look for broken connections, signs of excessive heat
Smell for overheating
Check power source
Trace path of logic through circuit
Know the normal operation of the circuit

22. QUIZ
1. The first three steps in troubleshooting are the use of your senses to (1) feel the top of the ICs for overheating, (2) to __________ for broken connections, and (3) to smell for signs of overheating.
look
2. The forth step in troubleshooting is to use a simple handheld instrument called a __________ to check the power sources at each IC.
logic probe
3. Your knowledge of the normal operation of the circuit and equipment is very important in troubleshooting. (True or False)
True

23. REVIEW Overview of Counters Characteristics of Counters
Ripple Up Counter
Ripple Counter with Waveforms
Ripple Down Counter
Self-stopping Counter
Frequency Division using Counters
Using Counter ICs
Magnitude Comparators
Troubleshooting Hints