how to eliminate initial state of counter

[jon_brutal]

how to eliminate input F

Hi everyone

this is a counter i made

F,b,a,9,8,7,6,5,4,3,2,1,0,F,b...

i intend to make a counter which i s

b,a,9,8,7,6,5,4,3,2,1,0,b,a,9,8,7,6,5,4,3,2,1,0,b

i need to remove the F, how do i do this. here is the circuit..can someone help me to fix this...thank you.im attaching the multisim file for editing.

 

[jumper2high]

Re: how to eliminate input F

If you are familiar with JK Flip-Flops and basic minimization techniques, you should write out all the 'transitions' and then work out which of the four FF's inputs need to be at which logical level to make the transition happen.

For example, you want to go from B to A, that means from 1011 to 1010, right? That means the first FF (for the lowest bit) needs to go from 1 to 0, so K needs to be 1, and J can be either 0 or 1. The second FF needs to go from 1 to 1 (ie keep previous state) which means for that one K must be 0 and J can be either 1 or 0, and so on.

Once you write out the truth table for the whole system, you can use the Karnaugh tables (cards/maps) to minimize it and get the desired result. The whole deal requires a fair bit of work if you do it manually, and I didn't have the time to work it out exactly yet...but you should be able to make it work if you know the basics.

Added after 23 minutes:

Had some time to kill, so I worked it out for you... (not guaranteed 100% correct)

I've labeled the four bits of binary as D, C, B and A so:

D C B A
1 0 1 1 <-b
1 0 1 0 <-a
1 0 0 1 <-9
1 0 0 0 <-8
.....
....
...
..
.

and the corresponding JK FlipFlops' inputs and outputs are named after that as well, so we've got

Jd, Kd, Qd and ~Qd
Jc, Kc, Qc and ~Qc
Jb, Kb, Qb and ~Qb
Ja, Ka, Qa and ~Qa

Now:

Ja = 1
Ka = 1
Jb = ~Qa
Kb = ~Qa
Jc = ~Qb * ~Qa * Qd
Kc = ~Qb * ~Qa
Jd = ~Qb * ~Qa * ~Qc
Kd = ~Qb * ~Qa

You'll notice that "~Qb * ~Qa" appears in a few places, so it's a good idea to do that separately and then AND it with Qd or ~Qc where needed.

 

[jon_brutal]

Re: how to eliminate input F

thank you,really great ide, once i try it out will let you know the results.

thank you again, really helpful.