Lecture 3.1.1  3.1.2
                      UNIVERSITY INSTITUTE OF ENGG.
UIE ACADEMIC UNIT 2
Bachelor of Engineering 
(Computer Science & Engineering) 
 Digital Electronics 22ECH-101
Counters DISCOVER . LEARN . 
EMPOWER
Counters
Course Outcome 
CO  To identify the different types of digital circuits and their difference and to 
1 illustrate the various types of gates.
CO To understand the various elements of digital system and to implement their 
2 applications.
CO To illustrate the relation between Combinational & Sequential Circuits and to 
3 apply for practical applications.
CO To solve the basic problems related to different types of digital circuits and to 
4 calculate it using various numerical problems.
CO To create different  hardware and software based digital applications. 
5
2
Definitio
n
• Counter : A sequential circuit that goes through prescribed  sequence 
of states upon the application of clock pulse is  called a counter.
• The input pulses are called count pulses, may be clock pulses  or they 
may originate from an external source or occur at  prescribed intervals or 
at random.
• In a counter the sequence of states may follow binary count  or any 
other sequence.
• Counters are found in almost all equipment containing digital  system
Binary Counter
• Binary Counter : A counter that follows the binary  sequence is called a 
Binary counter.
• An n-bit Binary Counter consists of n flipflops and  can count in binary from 
0 to 2n-1.
• For eg. Binary counter for two digits is as follows:
1
Presen Stat Nex Stat 00 01
t  A e  t  e  
B A B
1 1
0 0 0 1
0 1 1 0
1 0 1 1 1
1 1 0 0 11 10
Example of binary counter
• Here’s the another example for binary counter and its state  table:
Present State Inputs Next State
0  Q1  Q0  X  Q1 Q0
00 01 0 0 0 0 1
1 0 0 1 1 1
0 1 0 1 0
0 1 1 0
0 1 1 0 0
1 1 0 0 1 1
11 10 1 0 1 0 1
0 1 1 0 0 0
1 1 1 1 0
Applications of Counters
• Some of the applications of counters in a  sequential circuits 
are as follows:
 To count the number of occurances
 Generating Timing sequences
 Count up or down
 Increment or decrement count
 Sequence events
 Divide frequency
 Address memory
 As temporary memory
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.
Few other categories of 
counters:
• Apart from synchronous and asynchronous  counters which are the major 
ones the other  types of counters are as follows:
– Ring counter
– Johnson counter
– Decade counter
– Up–down counter
Asynchronous Counters:
• Here flipflop output transition serves as a source for  triggering other 
flipflops.
• This means that that the clockpulse is provided to a  single flipflop
• The change of state of a given flipflop is dependent  on the states of 
other flipflops.
• In other words the flipflops are not triggered by  simultanous clock pulses 
but the transitions in other  flipflops.
Asynchronous Counters
• This counter is called  asynchronous 
because not all flip  flops are have 
the same clock.
• Look at the waveform of the  output, 
Q, in the timing diagram.  It 
resembles a clock as well.
• This provides a clock that runs  
twice as slow. If we feed the  clock 
into a T flip flop, where T is  
hardwired to 1. The output will  be a 
clock who's period is twice  as long.
Four-bit asynchronous counter
• The external clock is  connected to the clock  input of the first flip-flop  only.
• So, it changes state at the  negative edge of each  clock pulse, but the next  
flipflop changes only  when triggered by the  negative edge of the Q  output of 
the first one.
State Sequence
Timing Diagram
Asynchronous counter
• Usually, all the CLEAR inputs are connected together,  so that a single pulse 
can clear all the flip-flops  before counting starts.
• The 2-bit ripple counter circuit above has four  different states, each one 
corresponding to a count  value.
• Similarly, a counter with n flip-flops can have 2N states.
• The number of states in a counter is known as its  mod (modulo) 
number.
 Two-bit asynchronous counter
• Thus a 2-bit counter is a mod-4 
counter.
• This is because the  most 
significant flip-flop  produces one 
pulse for  every n pulses at the  
clock input of the least  significant 
flip-flop .
3 bit asynchronous “ripple” 
counter  using T flip flops
• This is called as a ripple  
counter due to the way the  
FFs respond one after  
another in a kind of  rippling 
effect.
Up/Down Counter

Explanation of Up 
counter – 
Case 1 – When M=0, then M’ =1.
Put this in Y= M’Q + MQ’= Q So Q is acting as clock for next FFs. 
Therefore, the counter will act as Up counter.  
 
• The 1st FF is connected to logic 1. Therefore, it will toggle for every 
falling edge.
• The 2nd FF input is connected to Q1.Therefore it changes its state 
when Q1= 1 and there is falling edge of clock.
• Similarly, 3rd FF is connected to Q2. Therefore, it changes its state 
when Q2= 1 and there is falling edge of clock.
• By this we can generate counting states of Up counter.
• After every 8th falling edge the counter is again reaching to state 0 0 0.
Therefore, it is also known as divide by 8 circuit or mod 8 counter.
Explanation of Down 
counter
• Case 2 – When M=1, then M’ =0.
Put this in Y= M’Q + MQ’= Q’.  So Q’ is acting as clock for next FFs. 
Therefore, the counter will act as Down counter.
• The 1st FF is connected to logic 1. Therefore, it will toggle for every 
falling edge.
• The 2nd FF input is connected to Q’1.Therefore it changes its state 
when Q’1= 1 and there is falling edge of clock.
• Similarly, 3rd FF is connected to Q’2. Therefore, it changes its state 
when Q’2= 1 and there is falling edge of clock.
• By this we can generate counting states of down counter.
• After every 8th falling edge the counter is again reaching to state 0 0 
0.
Therefore, it is also known as divide by 8 circuit or mod 8 counter.
Modulus-M (MOD-M) 
counter
• A modulus-M counter is a counter where M 
represents the number of states present in the 
counter. Here M