Description of triggers in terms of signals

In the previous article we showed that the transition from logical levels to logical signals allows us to significantly simplify the description of all combinational circuits, reducing them to single text sentences.
Today we will extend this approach to triggers, expanding the set of signals, which will also allow us to abandon truth tables when describing them.

Signals are not a universal replacement for 1 and 0 in all cases. our channel there are dozens of lectures where they are necessary for calculations, for example, DNF, Karnaugh maps, etc. However, in some cases, for example, when describing triggers, ones and zeros obscure the meaning, generating constructions like Q(t+1) and the like. All readers who believe that 1 and 0 are the only way to describe logical circuits, you can stop reading so as not to traumatize your psyche :), but before that, answer yourself 3 questions: Why is R (reset) of counters always performed by direct input, why is the CS (chip select) input always inverse, and what logical level (1 or 0) does the signal have on the unconnected input?

For everyone else, let's get started. In general, the voltage at the input of a logic element changes continuously and has the form:

The voltage below and above the red lines are designated by logical levels 1 and 0, but there are also transitions between them: the leading and trailing edges. Under the voltage graph are images of the inputs of the logical circuits RESPONDING to the corresponding part of the pulse. Thus, real logical elements have 4 types of inputs.

As in the first article, we will say that there is a signal at the input if the corresponding part of the pulse has arrived at itThis approach expands the number of signals to 4, according to the number of different types of inputs, and allows us to describe logical circuits in a natural way.

Let's move on to triggers.
A trigger is a device that, in the absence of input signals, can remain in one of two stable states indefinitely.
A trigger is said to be set if there are signals at its outputs and reset if there are no signals at its outputs.

Fig. 2 shows the simplest triggers on 2OR-NOT and 2AND-NOT circuits, differing only in the types of inputs, but not in the operating principle. Everywhere below we will talk about triggers, ignoring the specific type of inputs, describing their operation in one sentence.

RS trigger is a trigger that is set by a signal at the “S” input (set) and reset by a signal at the “R” input (reset).

D trigger – a trigger that sets its state in accordance with the D input
at the moment the signal arrives at input C.

T trigger – a trigger that changes its state for each signal at the input T.

Synchronous RS trigger – a trigger that is set by S&C signals and reset by R&C signals.

JK trigger – trigger with inputs J,K,C, triggers only on signal at input C,
works similarly to a synchronous RS trigger, and when J=1 & K=1 it switches like a T trigger.

Other types of triggers can be described in a similar way, regardless of the number of outputs (1 or 2) and direct or inverse inputs.
It is much easier for a person to operate with one sentence than with voluminous truth tables when describing such simple elements.

If you have read this far, you can watch the short video on our channelwhich, in particular, shows how to experiment with such elements on a simple simulator.