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+14 votes
Design a synchronous counter to go through the following states:

$$1, 4, 2, 3, 1, 4, 2, 3, 1, 4 \dots $$
asked in Digital Logic by Veteran (59.9k points) | 901 views

I think $, D, JK or SR-Flip Flop$ any one of them could be used.

What is your opinion Praveen Saini ji ?

why cannot we do this via 2 FF only?Make a transitions from 0,3,1,2 and make a function to add 1 to each value that will turn into 1,4,2,3 counting ffs.If we have 3 FFs problem is we need to ensure so that it does not go into some unused state and doesn't return back to our used states....

@Surajit ji, Your opinion looks elegant and correct.


@Surajit brother can you please show via diagram ,your approach by using only two FFS

2 Answers

+16 votes
Best answer

Sequence given is as

$ 1,4,2,3,1\ldots$

From the given sequence of states we can design the state table and Suppose we are using T-FF for sequential circuit of counter.

Present state Next State FF Inputs
$A$ $B$ $C$ $A^+$ $B^+$ $C^+$ $T_A$ $T_B$ $T_C$
$0$ $0$ $0$ $x$ $x$ $x$ $x$ $x$ $x$
$0$ $0$ $1$ $1$ $0$ $0$ $1$ $0$ $1$
$0$ $1$ $0$ $0$ $1$ $1$ $0$ $0$ $1$
$0$ $1$ $1$ $0$ $0$ $1$ $0$ $1$ $0$
$1$ $0$ $0$ $0$ $1$ $0$ $1$ $1$ $0$
$1$ $0$ $1$ $x$ $x$ $x$ $x$ $x$ $x$
$1$ $1$ $0$ $x$ $x$ $x$ $x$ $x$ $x$
$1$ $1$ $1$ $x$ $x$ $x$ $x$ $x$ $x$

From the above table , we will find the equation of $T_A$, $T_B$ and $T_C$


answered by Veteran (55.8k points)
edited by
Is it necessary to cover all the possibilities? I mean we can only make the k-map for 1->4->2->3 and then i can find the Input expression for all three flipflops.
Need to fill at minterm loc in kmap while finding expression.
since there are 4 distinct states ( 1,4,2,3 ) can we use only two flipflops?

 Tuhin Dutta   HOW?


If we use ripple or jhonson counter we can make it, right? Since for k FF we can have 2k or 2k states respectively.

@Tuhin, you are right.
Might we need some extra logic gate to represent state 4?
Thanks for clarifying it, sir.
here sequence is given then why are you not following the given sequence only like (1 4 2 3 1 4 2.......).

means why are you covering all like(1 2 3 4 5 6 7 ).
ripple is asyhnchronous it s asking about synchronus
@rajoramanoj,   from state sequence we get state 4 where we need 3 bits to represent,100, with 3 bits we have 8 combinations 0 to 7, those state are not in sequence are unused states, for those next state is shown as dont cares.

Hi @Praveen Saini ji,

Thanks for your valuable effort. But to make circuit more error tolerant instead of using DO NOT CARE. We should move to some valid state from Invalid state. 

why Tb is not A+BC?

why B XNOR C??

acc to me Tb should be A+BC.

@Chhotu @Praveen Saini
Can we implement any sequence of 4 distinct states 

With 2 FFs

like 0,7,1,9,0,7,1,9.. ?


@jatin khachane 1 check this question.

We can have log n FF for n states. We just have to design the combinational circuit which will provide the appropriate input during next clock cycle to count those many states. 

Yes thats right ..but here to represnt 7 ..we need 3 bits ..1 FF output ==> 1 bit

eg 2 FFs ..FF1 ==> Q0,...FF2 ==> Q1
yes correct. depends on input. 😊
0 votes

Generally synchronous counter are designed by using D- flip flop and asynchronous counter are designed by using T- flip flop. So here counter designed by using D flip-flop

answered by (293 points)
D1=not(Q0) only

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