Counters

Types:

  • Synchronous counter
  • Ripple counter
Definition:
  • Synchronous counter: All the flip-flops are fed from the input clock.
  • Ripple counter: Cascade connection of Flip-Flops (each FF feeds the clock of the following FF).
Example of designing mod 8  synchronized counter:
We want to count 8 states ---> we need 3 FF to hold the states 2^3=8. States – Y0, Y1, Y2
State table:
 
Y0
Y1
Y2
Z(y1,y2,y3)
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
0
1
1
1
1
  •                                                           The T-FF :

    • T
    Q(t+1)
    0
    Q(t)
    1
    Q`(t)











    Computing the input of the T  FF’s: 

             y1 y2
	 _______________________ 
	             |   | 00  01  11   10       t0 = y1y1
	 |---|------------------ 
y0   | 0 | 0   0   1    0
     | 1 | 0   0   1    0

         y1 y2
	 _______________________ 
	            |   | 00  01  11   10       t1 = y0
	 |---|------------------ 
y0   | 0 | 0   1   1    0
     | 1 | 0   1   1    0

         y1 y2
	 _______________________ 
  	           |   | 00  01  11   10       t2 = 1
	 |---|------------------ 
y0   | 0 | 1   1   1    1
     | 1 | 1   1   1    1


    


Z=y2 y1 y0 because it
gets 1 only when y0, y1, y2 are 1.

    
Implementation:

    



    


    Creating a mod
64 counter from two mod 8 counters:

    

    
Up-down counter:

      

    • 
Control bit U/D` - U/D`
= 1 --> up-counter
      • 


    • 
 U/D` = 0 --> down-counter
      • 

    


    


    Implementing up/down counter:

    


      

    • 
x=0   up counter
      • 


    • 
x=1 down counter
      • 

    
            
y1  y0

               
----------

          a=  
0    0

          b= 

0    1

          c=  
1    0

          d=  
1    1

        y1   y0     
x     Y1    Y0

    -----------------------------------

        0     
0      0      0     
1

        0      
0     1      1     
1

        0     
1      0      1     
0

        0     
1      1      0     
0

        1     
0      0      1     
1

        1     
0      1      0     
1

        1     
1      0      0     
0

        1     
1      1     1      
0

    

                    
y0 x

             ____________________

            |     
|   00   01   11   10

            |--- |----------------------

       y1 | 0   |   1     
1      1     1

            | 1   |  
0     0       0    
0

                       
t0=y0'

                  
y0 x

             ____________________

            |     
|   00   01   11   10

            |--- |----------------------

       y1 | 0   |   0    
1       0     1

            | 1   | 
1     0        1    
0

                 
t1=y0 xor y1 xor x

       
Decimal counter: ( Non synchronized)

    

    It is also easy to construct synchronized decimal
counter

                                                         
Timing diagram:

    


    Divider by n:

    Every n rises of the input clock, the
divider gives a single rise at the output.

    

    

    

    

     Divider by 2:

    Divider by 4:
    

    

    

    

    


    
This is a non
synchronize divider- the clock to the second FF comes from the first 
FF.