Everyone has used the calculator. Have you ever thought about how it was implemented? Here I will not detail the principle of the calculator, but only a brief introduction to the idea. When we learn the microcontroller, we can also make a calculator by hand. What should I do with mathematical calculations through the circuit? For the sake of understanding, let me give you a very simple example.
  
In this circuit, the resistor R1=R2, I connect the two points A and B to 3V and 5V respectively. At this time, the voltage at point C is (5+3)/2=4V. This circuit performs an averaging operation. If we use 1V to represent the number 1, it calculates that the average of 3 and 5 is 4; if we define 1mV to represent the number 1, the circuit calculates the average of 3000 and 5000. The value is 4000. If I can design many circuits like this by clever methods, using resistors and capacitors and other components of the transistor, it can perform very complex four operations, as well as square, square, logarithmic and other operations. This is a simple example of using circuits to help us with mathematical calculations. In this case, it is not necessarily reflected in the advantages of circuit calculations compared to our calculations using pen and paper. But if we make the circuit complex enough, its calculation speed is quite fast, and as long as there is power supply, it will never tire tired calculation, and it is not easy to make mistakes.
Above we have designed a simple analog circuit calculator that calculates the average of two numbers. We use voltage values ​​to directly represent numbers. But this circuit is not so ideal in practice. When doing basic electrical experiments to measure voltage, you will find that the voltage measurement always has errors, the voltmeter has errors, the readings are also error, and it is basically unavoidable. Many things in nature are error-prone. Here, in addition to the value measured by the voltmeter and the actual value, the actual C point voltage value is not exactly equal to the average of the AB voltage value, because it is difficult to ensure that the resistance values ​​of R1 and R2 are exactly the same, and the wire also has resistance. So the result we calculated is more likely to be 3.99 or 4.01 instead of the exact 4.00, which leads us to calculate the error. If the circuit is complicated, the error will gradually accumulate and become larger and larger, and finally the calculation result is completely meaningless, and it is not easy to reduce the error of the circuit.
So the digital circuit was born. Compared to the inaccuracy of analog circuits, digital circuits have great advantages. Note that digital circuits are relative to analog circuits, and the nature of digital circuits is also analog. Usually we mean analog circuits, which refer to circuits other than digital circuits.
We humans use decimal notation to represent numbers because we have ten fingers. In digital circuits, binary numbers are used for calculations because many electronic devices tend to have two very certain states, such as "on" and "off" of the switch, and "light" and "off" of the lamp. Binary numbers are actually much simpler than decimal numbers. In decimal, from 0 to 9, full 10 is carried to the high position, that is, 9+1=10; and the binary is full two, so 1+1=10 in the binary. At first we would feel that this is very awkward. In fact, it is not how difficult binary is, but we are used to decimal.
In digital circuits, we use a more common way to represent binary digits by voltage, called TTL level (TTL = Transistor-Transistor Logic, originally intended as logic gate). It stipulates that the +5V voltage is high, indicating the number "1", and the 0V voltage is low, indicating the number "0". Due to the characteristics of the circuit itself, the voltage output by the TTL level circuit is not absolutely accurate 5V and 0V, but it is specified that the voltage of >2.4V is regarded as a high level, and the voltage of <0.4V is regarded as a low level. . It is precisely because of this feature that we do not need to control the voltage very accurately, we can accurately represent the number we want to represent. Compared with the previous analog average calculation circuit, it is obviously advantageous. This is also the root cause of the widespread use of digital circuits.
The introduction of digital circuits ends here, and there will be a more detailed introduction in the principle chapter. In fact, the essence of microcontrollers is also digital circuits. The traditional digital circuit we will refer to below refers to digital circuits other than programmable devices such as microcontrollers. Let's take a look at the difference between a microcontroller and a traditional digital circuit.
Using some common traditional digital circuit devices (generally integrated circuit chips), we can design the circuit as shown below. It is an electronic watch with six digital tubes showing the time, and the figure is showing 00:00:18. It can be seen that this circuit is still quite complicated and designed to be time consuming.
  
However, the emergence of single-chip microcomputers makes the design of circuits that achieve the same function much less difficult. The figure below is a circuit designed using a microcontroller. The same is the electronic watch, not only the display effect is better than the previous one, but also the function is more powerful, the two buttons can adjust the time and date like the two buttons on the market, and the circuit is much simpler. We only need to write the specific program to the microcontroller, so that it can work in the way we designed.
If one day, we want to add the function of the timepiece to the electronic watch, for the previous digital circuit, I am afraid that the whole circuit has to be redesigned; but for this circuit made by the single chip, we only need to modify the program code, then Re-write it in, just like installing software on a computer, there is no need to modify the circuit, it is very convenient.
  
The relationship between traditional digital circuits and microcontrollers is like the relationship between non-smart phones and smart phones. The biggest advantage of smart phones is that they can install a variety of software games, and not a smart phone does not have such powerful features. The same is true for single-chip microcomputers. You can download various programs for it and let it work according to your ideas. For the microcontroller, the hardware circuit is the body of the microcontroller, and the program is its soul, and you are the God of writing the program.
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