is it possible to make asynchronous down counter modulo 6 with 3 JK flip-flop?

Question

in last week lab classes with my lecturer, we were asked to make an asynchoronous down counter mod 6 using jk flip-flop, but no one could make it until the end of the class. all of us has the same opinion, that the ff must be reset when the output is 111 (desired output: 101 100 011 010 001 000) by using NAND 3 input gate (input is QaQbQc where Qc is LSB) and output of NAND connected to CLR' of second ff. but our output is all the same, it stuck in 100 101 100 101 100 101 ...

so after i go home i tried again using proteus. and after analyzing, i understand that: when switching from 100 tp 011 what happen is:

out comment
100 clk down Qc next=1,Qb next=hold,Qa next=hold   
101 Qc' down Qb next=1,Qa next=hold   
111 NAND gate is false, thus Qb reset   
101 so the next state of 100 will never be 011

i think the third flip flop will never catch clock (Qb' from previous ff) since the previous ff is forced to reset before the third flip flop could "read" the inputed clock.

so is there really a way to make asynchronous down counter FF using 3 JK flip flop?

the circuit we designed: https://i.sstatic.net/DrYjD.png

Answer 1

Your configuration is theoretically correct but when configured correctly as a down counter there is still a problem. When the counter transitions from 100 to 011 there will be an intermediate glitch state of 111 at the outputs which is the state the NAND gate detects. So when transitioning from 100 to 011 the counter will jump to 001 (the middle bit has been incorrectly reset). So the sequence will be 000 101 100 001 000 and repeat.

You may think that it is possible to detect the state 000 with an OR gate and feed its output to the J input of the second stage (with K=1) thereby freezing the middle flip flop at Q=0 for the next CK rising edge but this would prevent a rising edge reaching the CK input of the most significant stage which will produce 001 at the outputs instead of 101.

So all in all I don't see how it's possible to design an asynchronous mod6 down counter using JK flip flops and simple techniques. I'd be very interested to see if anyone can do it and the technique used.

To give you an example of a synchronous mod 6 down counter. This design also caters for the two unused states, 110 and 111. If either of these two states should occur, perhaps at power up, then the counter will be sent to state 000.

Answer 2

The counter should have binary state sequence 5, 4, 3, 2, 1, 0, 5, 4, 3, 2, 1, 0, 5, etc... Only 6 states, surely they can be stored in 3 JK-ffs. A non-optimal way is to make a counter which starts from 0 and counts to 6 which is set to clear the counter. There's a momentary 7th state. But we decode the binary states 0,1,2,3,4,5,6 with a big combination circuit to decreasing series 5,4,3,2,1,0,0. The extra short living seventh state is decoded to an allowed state, too.

The result isn't free of wrong short living states. That would need a cyclic code in the base counter and race-free decoder.

Answer 3

Synchronous Down Counter Modulo-6

Schematic

Simulation