how to design a circuit that gives high output between input transition and next rising edge of CLK

Question

I'm trying to understand how can one build a circuit that does the following functionality:

I see according to the output that I should have a D-FF, that works at Falling-Edge mode, so I need to add an inverter to the CLK. how can I continue from here? are there basic rules that I can follow in order to know what should I add more?

Note: my intention is to use D-FF in the circuit. I have knowledge in designing mealy machines and aware of the procedure. but here the states aren't quiet clear in order to make mealy machine design. I would like to know if this could be a successful approach for the problem. the reason I thought about mealy machine is because the output change is dependent of the input change.

Answer 1

An edge detector like this should do the trick: dual edge detector

If the output falling edge needs to be synchronized with the rising edge of the clock, then feed the pulse output into the clock input of a D-Flop and the input clock to the reset input of the D-Flop. D input is tied high. The example circuit assumes the D-Flop uses low for reset. If high for reset type, then NOT3 gate can be removed.

^{simulate this circuit – Schematic created using CircuitLab}

Answer 2

You could consider starting down the route of an edge detector using an EXOR gate: -

That gives you a kick in the right direction by producing a pulsed output each time IN changes state. If you need to extend the pulse, use a monostable or, if it should extend only as far as the next positive going CLOCK edge then use a D type flip flop to latch the pulse and clear it on the rising clock edge.

Picture also available in this answer.

Answer 3

You're delving into the realm of asynchronous state machines, a tricky but very interesting part of digital logic design. Essentially you need some basic combinatorial logic combined with some asynchronous feedback. If you look at the internal structure of a flip flop (at least the historical method of construction) it's essentially some cross-connected NAND gates with feedback.

The text I used as a reference is by David J. Comer, "Digital Logic and State Machine Design". In the last chapter or two, asynchronous design is covered in detail.

Your waveforms don't specify every possible transition case, so I made a few assumptions about what you want, then came up with this state feedback table, reduced expressions, and a circuit that implements it without any explicit flip-flops.

The state table (might need adjustment to change my assumptions):

When the value in the cell of the Karnaugh map matches the value on the left side of the table, you are in a "stable state". An asterisk (*) in the table indicates that the output signal should be high in that state. When the value inside the table is different than the value at the left side of the same row, the state is unstable and the state machine will change to the row number indicated inside the state cell. For example, when both signals are low, we start in the top left corner (and YZ also equals 00). When the "IN" signal goes high, we move one cell to the right in the Karnaugh map, where the value of "01" takes us to the second row (where YZ are "01"). Since that cell also contains "01," the state is stable. The asterisk in that cell indicates that the output should be high, and so on.

Apologies for any small errors, I didn't have a chance to simulate the full circuit, but the general approach is valid.

It's this kind of complexity that typically drives us to do fully synchronous design, because it's easier to design and analyze.