The document outlines the introduction and functioning of synchronous and asynchronous counters, focusing on the operation of flip-flops and the steps required to design a synchronous counter. It includes detailed steps for creating 2-bit and 3-bit down counters, including determining the number of flip-flops, writing excitation tables, state diagrams, and logic diagrams. Synchronous counters are highlighted for their ability to operate at higher frequencies due to simultaneous clocking of flip-flops, minimizing propagation delay.

3. Index
No. Title
1 Introduction of Counter
2 Synchronous Counter
3 Steps 1 to 7
4 2-Bit Synchronous Down Counter
5 3-Bit Synchronous Down Counter
6 Application

4.  A counter is a sequential circuit that goes
through a predetermined sequence of
states upon the application of clock
pulses.
 Counters are categorized as:
 Synchronous Counter:
All FFs receive the common clock pulse, and
the change of state is determined from the
present state.
 Ripple(Asynchronous) Counters:
The FF output transition serves as a source for
triggering other FFs. No common clock.

5.  All the flip-flop are clocked simultaneously.
 Synchronous counters can operate at much higher
frequencies than asynchronous counters.
 As clock is simultaneously given to all flip-flops there is no
problem of propagation delay. Hence they are high speed
counters and are preferred when number of flip-flops
increase's in the given design.
 In this counter will counter

6.  Step 1: Determine the number of flip-flop needed.
 Step 2: Type of flip-flop to be used.
 Step 3: Write the excitation table for the flip-flop.
 Step 4: Determine the state diagram.
 Step 5:Make excitation table for the counter .
 Step 6: K-map simplification.
 Step 7: Draw the logic diagram.

7.  Step 1:
Flip-flops required are
2 𝑛 ≥ N
Here N=4 so No of flip-flop is required is 2.
 Step 2: Here we will us JK flip-flops.
 Step 3: Excitation table for the JK flip-flop
𝑸 𝒏 𝑸 𝒏+𝟏 J K
0 0 0 X
0 1 1 X
1 0 X 1
1 1 X 0

8.  Step: 4
State Diagram

9.  Step: 5
Excitation table for the 2-bit down counter .
Present state Next state Flip-Flop input
𝑸 𝑨
𝑸 𝑩 𝑸 𝑨 + 𝑸 𝑩 + 𝑱 𝑨 𝑲 𝑨 𝑱 𝑩 𝑲 𝑩
0 0 1 1 1 X 1 X
0 1 0 0 0 X X 1
1 0 0 1 X 1 1 X
1 1 1 0 X 0 X 1

10.  Step: 6
K-map simplification.

11.  Step: 7
Draw the logic diagram.

12.  Step 1:
Flip-flops required are
2 𝑛
≥ N
Here N=8 so No of flip-flop is required is 3.
 Step 2: Here we will us T flip-flops.
 Step 3: Excitation table for the T flip-flop
𝑸 𝒏 𝑸 𝒏+𝟏 T
0 0 0
0 1 1
1 0 1
1 1 0

13.  Step: 4
State Diagram

14.  Step: 5
Excitation table for the 3-bit down counter .
Present state Next state Flip-Flop input
𝑸 𝑨 𝐐 𝐁 𝐐 𝐂 𝐐 𝐀 + 𝑸 𝑩 + 𝐐 𝐂 + 𝐓 𝐀 𝐓 𝐁 𝐓𝐂
0 0 0 1 1 1 1 1 1
0 0 1 0 0 0 0 0 1
0 1 0 0 0 1 0 1 1
0 1 1 0 1 0 0 0 1
1 0 0 0 1 1 1 1 1
1 0 1 1 0 0 0 0 1
1 1 0 1 0 1 0 1 1
1 1 1 1 1 0 0 0 1

15.  Step: 6
K-map simplification.

16.  Step: 7
Draw the logic diagram.