Designing a 4-bit non-sequential synchronous counter

I am working on a 16:4 MUX that is comprised of four cascaded 4:1 MUXs. Each MUX has an active-low enable pin. To enable one MUX at a time, I need to use a counter that outputs the following:

Clock Cycle 1: 1110
Clock Cycle 2: 1101
Clock Cycle 3: 1011
Clock Cycle 4: 0111

In decimal, the clock is counting from 14 to 13 to 11 to 7 and then repeating.

I've generated a state diagram, a next-state table, a J-K FF transition table, the appropriate K-maps based on these tables, and finally a set of minimized SOP expressions from the K-maps. However, my output pins (Q₀, Q₁, Q₂, and Q₃) are all high all the time. I don't understand why.

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My tables, K-Maps and SOP expressions are here: **broken link removed**

What are the status of the Clr and preset inputs if they are not proper the ops will always be 1 irrespective of the inputs

JJBladester said:

my output pins (Q₀, Q₁, Q₂, and Q₃) are all high all the time. I don't understand why.

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I don't see where you initialize the 1^st state (1110). It could be any state.

jeffrey samuel said:

What are the status of the Clr and preset inputs?

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I have the active-low ~CLR pin set high.

This is the output I get. The Q outputs of all four J-K flip-flops are low until the first positive clock transition at which point they go high and stay high.

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I think the last Preset and the clear pins are causing havoc in your design do rectify them to remove your trouble

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There is some error in the design part

each ff has J=1 and k=~Qn-1

IF so the input combination in all the cases are 10 in the JK and the corresponding ops are Qn=1 and ~QN=0

The 74107N J-K flip-flops I'm using don't have a SET pin. From the logic analyzer output I included in my previous update, you can see that all outputs are initially 0. MultiSim, the software I'm using, has 74109N J-K flip-flops with active-low ~PRE (preset) pins. How do I push an initial value to those pins once and then keep them high for the remainder of the circuit operation? Would a set of one-shot's work?

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jeffrey samuel said:

There is some error in the design part

Each FF has J=1 and k=~Qn-1 so the input combination in all the cases are 10 in the JK and the corresponding ops are Qn=1 and ~QN=0

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I must be making an incorrect assumption when grouping cells on my Karnaugh maps, then. I've gone over them more than a handful of times and the 0's, X's, and 1's are in the correct places. Specifically for my J₀, J₁, J₂, and J₃ maps... Is it correct that I am grouping all cells on those map to make all J inputs equal 1?

Just keep the preset pin high through out the operation that should solve your issue I guess

The K maps are fine to the best of my knowledge

JJBladester said:

MultiSim, the software I'm using, has 74109N J-K flip-flops with active-low ~PRE (preset) pins.

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74109 FFs work differently than 74107 FFs: the former have ~K (i.e. inverted K) inputs.

JJBladester said:

How do I push an initial value to those pins once and then keep them high for the remainder of the circuit operation?

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Use an appropriate pulse source (initial value longer than the 1^st active clock edge).