How to make a digital number detector

Digital electronics is one of the most important fields of today's world because it offers us a great deal of technological freedom. Without it, we would not have inventions as commonplace today as the telephone or the radio. In the article by today we will explain some basic principles of digital electronics and use them to build a simple number detector. (from 0 to 9).

The first thing we need to know is what is a truth table. This is the basis of all digital electronics as it contains all the possible reactions of our circuit.

Truth table

As you can see, the first thing you can see in the image is that the digital electronics are all made in binary code. In addition, like any other circuit in any field, it has a series of tickets which provide stimuli (A3,A2,A1,A0) and a series of outlets provided by the effects (S). In the case of our detector we can see in the image that whenever the inputs contain a number in the inputs that is less than 9 in binary (from 0000 to 1001) in the output we will obtain a 1, that is to say, it will be active. Otherwise we will get a 0, i.e. it is not active.

The next step is to extract the equation. Una forma de hacerlo es mediante los 1 de la salida. Cada 1 se corresponderá con una parte de la función. Por ejemplo el primer 1 se corresponde con: A3’A2’A1’A0′. Como veis cuando la entrada es 0 se escribe A’ y cuando es 1 se escribe simplemente A. La ecuación seguiría: S = A3’A2’A1’A0′ + A3’A2’A1’A0 + A3’A2’A1A0′ + …

As you can see, the final expression is going to be quite long, so there are a series of simplification rules that allow us to obtain a great simplicity in the equations. These rules are as follows:

Simplification rules

With these expressions we will get an equation like the following:

S = (A1’*A2′)+A3′

Finally, it is also important to know what are the timetables as they are also quite useful. A timeline is nothing more than a graph in which all possible states of inputs and outputs are represented. It is the same as a truth table but in graphical form. Here is the timeline of the logic function of our number detector:

Timeline

Remember that, as always, you can use our forum to answer any questions you may have.

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