# How to realise this transition based truth table

#### SpannerSpark

Apr 3, 2014
1
Hi all,

I am puzzling how to realise the truth table (see attached) in logic hardware.
A and B are the 2 inputs to the circuit and Z is the resulting output.
Essentially any inputs rising or falling edge overrides the previous state.
I can draw the truth table so I guess it is possible to design the circuit.

I know that I need to use edge triggered building blocks (i.e J-K flip flops or similar) but I cant get my head around how to do it. As its not state logic, but instead based on transitions, I cant do standard boolean algebra/karnaugh maps etc. Any help gratefully received.

#### Attachments

• TruthTable1.jpg
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#### Harald Kapp

##### Moderator
Moderator
Nov 17, 2011
12,722
I will move this thread to the homeworks section - where I strongly believe it belongs.
I will also not provide the full answer but I will guide you to finding it yourself.

You can simplify the table by noting that for any transition of A or B (h-l or l-h) the state of the other signal is actually irrelevant.

To register an edge you feed it to the clock input of a flipflop. Since a flipflop is sensitive to one edge only (typically l-h), you need to invert A and B to create A# and B# which have rising edges instead of falling edges.
You now have 4 signals, namely A, B, A# and B# which all have active rising edges.

- What is the number of flipflops you need to register any of these edges?
- How can you achieve that the output for the flipflops registering A and B edges go high, the outputs of the flipflops registering A# and B# go low?
- How can you ensure that a falling edge on one signal prepares the respective flipflop for the rising edge for registering the next edge?
- How can you create Z from the outputs of these flipflops?

Note1: I envision a solution using D Flipflops with Reset and Set inputs.

Note 2: that the table implicitly assumes that no two edges appear simultaneously (simultaneously meaning within the setup and hold times of real flipflops).

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