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ENCYCLOPEDIA OF RADIO ELECTRONICS AND ELECTRICAL ENGINEERING Synthesis of digital circuits. Encyclopedia of radio electronics and electrical engineering
Encyclopedia of radio electronics and electrical engineering / Beginner radio amateur Such a serious institute name... Don't get scared ahead of time. Let's go in order. In electronics, the term "black box" is often used. This, of course, is not the black box that the Ministry of Emergency Situations is looking for after another crash of Aeroflot's Tu-154. Another box... In electronics, a "black box" is a kind of circuit that is lazy to draw. This circuit has some inputs, some outputs, and we know exactly how it behaves. That is, you can easily predict what will happen at the output if you apply something to the input. Roughly speaking, the black box circuit is described by a mathematical expression of the form: y = f(x), where x - input signal y - output signal.
Black boxes have just a lot of life examples ... Take at least such a trivial thing as an iron. It has a temperature adjustment knob and a steam release button - these are the "inputs" of the black box. Also, it has a heating surface, and in it - holes - these are "exits". How are inputs and outputs related?
This example may be rather primitive, but it is obscenely obvious. After all, in the morning, ironing trousers, you don’t think about how the iron works? But you know perfectly well what needs to be done with a pen and a button in order to get the desired result ... Why am I all this? And to the fact that in technology one often has to resort to the concept of a "black box" in order to simplify development at a certain stage. However, at subsequent stages, you still have to "unfold" the black box - that is, design its circuit. And since you and I bear the proud name of Electronics Engineers, and not just shareholders-tinkers, but also designers-developers, it is our direct duty to be able to come up with its scheme from the description of the black box. Of course, we will not make irons. Especially - in the section on digital technology. We'd better deal with the synthesis of digital circuits according to the truth table. Task number one There is a certain element with two inputs and one output, and its truth table is known:
It is necessary to come up with a diagram of this element based on known logical elements. We carefully look and think ... We are interested in those positions of the truth table in which the output signal is 1. BUT! Here's what we see: a unit at the input b in any case leads to a unit at the output. Great!
So we can connect the input b directly with the output c ... More precisely, they could. But we have one more unit at the output - when zeros are applied to both inputs. Remember which element reacts to two zeros? Let me look at the previous paragraph... That's right, the "OR-NOT" element! This means that the second unit will be formed by the OR-NOT element. Let's draw our own scheme for each case:
Now we need to combine these schemes into one. Please note that you cannot directly connect digital outputs. So you need to connect them through some element. Moreover, this element should give a unit to the output if at least one input has a unit. Well, what is this element? Of course, it is "OR". So:
That's the whole scheme. Pretty simple, right? Further worse. Task number is as follows The element to which you want to draw a diagram has three inputs and one output. Accordingly, the truth table increases automatically to 8 lines:
So what do you think??? Hmm, this is a little more complicated. But! It's not hard for us, is it? Then - forward and with songs! So, we select those lines in which the output signal = 1. There are only five of them:
Now let's draw a separate diagram for each selected line, using only the "AND" and "NOT" elements.
All! Now it only remains to combine these schemes into one. This will immediately reduce the number of inverters:
Well, okay? I explain: we made two groups of inputs - direct and inverse (that is, "reverse"), and connected the "AND" elements to these groups according to the schemes that we developed before. The output signals of the "AND" elements are mixed using a 5-input "OR" element. Cascading "AND" and "OR" elements As you can see, in the last circuit we used "AND" elements with three inputs and an "OR" element with as many as five inputs! Someone will probably have a question: what are their truth tables? It's all right, gentlemen! The "AND" element remains the "AND" element, even with 100 inputs. At its output, a unit is possible only if units are applied to all inputs. The same is true for the OR element. It will give a one if at least one input has a one, even if it has at least a thousand inputs. Such multi-input elements can be easily obtained from ordinary two-input elements by including them in a cascade circuit:
If you don't believe me - make a truth table for each "step" of the cascade - and check :) Publication: radiokot.ru
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Comments on the article: Alexander Good article. It clearly explains what and how it works. The only pity is that it is short, it would be possible to cover the topic more widely for us dummies.
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