Synchronous counter

[rds1975]

Hi

Can anyone guide me to solve this problem. Circuit picture is attached

The circuit diagram of a synchronous counter is shown in fig. below.
Determine the Sequence of states of the counter. Assume that the init ial state is 000. Give your answer in tabular form, showing the present state QA(n), QB(n) , QC(n) , J-K inputs (JA, KA, JB, KB, JC, KC) and the next state QA(n+1), QB(n+1), QC(n+1). From the table determine the modulus of the counter.

Thanks and regards

 

[carozoynarizota]

We have for a JK flip flop the following table:

J K Qn+1
0 0 Q
0 1 0
1 0 1
1 1 -Q

For FF A and B we have that K is always 1, so we can see the table sequence as:

J Q Qn+1
0 0 0
0 1 0
1 0 1
1 1 0

Then,

QA(n+1)=JA*[-QA(n)] but JA=-QB

QA(n+1)=[-QB(n)] * [-QA(n)]

QB(n+1)=JB*[-QB(n)] but JB=QA

QB(n+1)=QA(n) * [-QB(n)]

Finally for the third FF, J=K, so the table sequence will be:

J=K Q Qn+1
0 0 0
0 1 1
1 0 1
1 1 0

Now the last eq. is:

QC(n+1)={QB(n)*[-QA(n)]} ⊕QC(n)

where: J=K={QB(n)*[-QA(n)]}
⊕ exclusive or

Now we can build the table you need:

QA(n) QB(n) QC(n) QA(n+1) QB(n+1) QC(n+1)
0 0 0 1 0 0
1 0 0 0 1 0
0 1 0 0 0 1
0 0 1 1 0 1
1 0 1 0 1 1
0 1 1 0 0 0

From there you can build the complete table for all the variables the way you asked for and get its module.

Bye Bye
Sebastián

P.D.: check for mistakes.