Finding functions for JK / D / T flip flops

Question

I am trying to understand this concept of flip flops. Given some Karnaugh Map, all I need to know is how to find the functions of various flip-flop types:

• sr flip-flop (\$s = \text{ ??} \quad r = \text{ ??}\$)
• D flip-flop (\$D = \text{ ??}\$)
• T flip-flop (\$T = \text{ ??}\$)
• JK flip-flop (\$J = \text{ ??} \quad K = \text{ ??}\$)

I believe I know how to solve the sr flip flop but I am clueless about the others. I have created this random Karnaugh Map and solved for sr flip-flop.

If I wanted to explain it to someone I'd probably go with this:

In order to find s and r functions of sr flip flop, first mark all the bold 0s and bold 1s.

A cell is bold if the value inside that cell is different than the number of row that cell is in. (Here we consider only the a value of the row)

After you marked all the bold 0s and 1s, you need to group them.

All bold ones should be put into as large groups as possible. Only the bold ones need to be considered when grouping, however it is best to cover all non-bold ones if possible (as long as you don't introduce extra groups).

Here the result is one green group on the screen that covers all bold ones and as many non-bold ones as possible.

Then, the grouped ones correspond to s function. You simply calculate the Sum of Products.

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Now the bit tricky part: do the same with bold zeros, that is group them into as large group as possible.

And now you can find the r function either as:

• a). Product of Sums, and complement over everything

or

• b). treat the grouped 0s as 1s (imagine they're 1s) and find the function using SoP, without any extra complementation over everything. The result is the same.

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So to summarize: for sr flip flop s is function obtained by grouping bold ones (SoP) and r is function obtained by grouping bold zeros (PoS) and complementing everything afterwards.

I believe that's correct, Ph.D teacher confirmed that.

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Now back to my question: can somebody explain to me like I am 5 years old how to find D, T, JK flip-flop functions from some Karnaugh Map?

For example maybe J = bold zeros complemented, K = bold ones. Or something like that.

Thanks~!

Answer 1

It's not clear to me what you are trying to do. What do you mean by "solved for sr flipflop"? I've been doing and teaching digital systems design for a long time and I've never seen anything like this. What are the four inputs for your table? The link that jonk provided describes using K-maps to design the combinational logic that makes one kind of flip-flop "look like" a different kind of flip-flop.

Karnaugh maps are used to describe the functionality of combinational logic. They are not a good choice for use with latches and flip-flops. Latches and flip-flops can have different output values for a single input condition, which doesn't work with a Karnaugh map.

For bistable storage elements (latches and flip-flops) you should use a state table, where the next state is expressed as a function of the current state, the combinational input, and any edge-sensitive input.