Multiplexers and demultiplexers: operating principle, explanation with a simple example, application. Multiplexers and demultiplexers: circuits, operating principles Multiplexers and demultiplexers presentation
Multiplexer - called a combinational device that ensures the transmission in the desired order of digital information arriving through several inputs to one output. Multiplexers are designated through MUX (from the English multiplexor), as well as through MS (from the English multiplex or selector).
It can be schematically depicted as a switch that provides connection of one of several inputs (they are called information) to one output of the device. In addition to information inputs, the multiplexer has address inputs and, as a rule, permissive (strobe) inputs. The signals at the address inputs determine which specific information channel is connected to the output. If the relationship between the number of information inputs n and the number of address inputs m is n = 2 m, then such a multiplexer is called complete. If n< 2 m , то мультиплексор называют неполным.
Enable inputs are used to expand the functionality of the multiplexer. They are used to increase the multiplexer's capacity and synchronize its operation with the operation of other nodes. Signals at the enabling inputs can either allow or prohibit the connection of a specific input to an output, i.e., they can block the operation of the entire device.
Operation of a two-input multiplexer
Let's consider the operation of a two-input multiplexer (2 →1), which is conventionally depicted as a switch, and the state of its inputs X 1 X 2 and output Y is shown in the table (Fig. 3.41).
Based on the table, we can write the following equation:
Y = X 1 A + X 2 A
In Fig. Figure 3.42 shows the implementation of such a device and its conventional graphic symbol.
The basis of this circuit is two coincidence circuits on AND elements, which, at a logical level of “1” at one of their inputs, repeat at the output what is at the other input.
If it is necessary to expand the number of inputs, then use cascaded multiplexers. As an example, consider a multiplexer with four inputs (4 → 1), built on the basis of (2 → 1) multiplexers.
The diagram and state table of such a multiplexer are shown in Fig. 3.43.
Multiplexers are universal logical devices, on the basis of which various combinational and sequential circuits are created. Multiplexers can be used in frequency dividers, trigger devices, shifters, etc. Multiplexers are often used to convert parallel binary code into serial. For such a conversion, it is enough to apply a parallel binary code to the information inputs of the multiplexer, and apply signals to the address inputs in such a sequence that the inputs are alternately connected to the output, starting from the first and ending with the last.
Multiplexer as a shifter
Let's consider an example of using multiplexers to implement the so-called combinational shifter, which provides a bit-by-bit shift of a binary number. The operating principle of this device is clear from the device diagram and the table of states of its inputs and outputs (Fig. 3.44).
In the designation of multiplexers, two Russian letters KP are used, for example, the industry produces such multiplexers as K155KP1, K531KSh8, K561KPZ, K555KP17, etc.
A demultiplexer is a device in which signals from one information input arrive in the desired sequence through several outputs, depending on the code on the address buses. Thus, a demultiplexer is functionally the opposite of a multiplexer. Demultiplexers are designated by DMX or DMS.
If the relationship between the number of outputs n and the number of address inputs m is determined by the equality n= 2 m, then such a demultiplexer is called complete, with n< 2 m демультиплексор является неполным.
Operation of a two-output demultiplexer
Let's consider the operation of a demultiplexer with two outputs, which is conventionally depicted as a switch, and the state of its inputs and outputs is shown in the table (Fig. 3.45).
From this table it follows: Y 1 =X·A Y 2 = X·A i.e. such a device can be implemented as shown in Fig. 3.46.
To increase the number of demultiplexer outputs, cascade connection of demultiplexers is used. As an example (Fig. 3.47), consider the construction of demultiplexers with 16 outputs (1 → 16) based on demultiplexers with 4 outputs (1 → 4). 
If there are zeros on the address buses A 0 and A 1, the information input X is connected to the upper output DMX 0 and, depending on the state of the address buses A 2 and A 3, it can be connected to one of the DMX 1 outputs. So, when A 2 = A 3 = 0, input X is connected to Y 0. When A 0 = 1 and A 1 = 0, input X is connected to DMX 2, depending on the state of A 2 and A 3, the input is connected to one of the outputs Y 4 - Y 7, etc.
Demultiplexer functions
The functions of demultiplexers are similar to those of descramblers. The decoder can be considered as a demultiplexer, in which the information input maintains the output voltage in the active state, and the address inputs serve as decoder inputs. Therefore, the same letters are used in the designation of both decoders and demultiplexers - ID. They produce decryptors (demultiplexers) K155IDZ, K531ID7, etc.
When using CMOS technology, it is possible to build bidirectional switches that have the ability to pass current in both directions and transmit not only digital, but also analog signals. Thanks to this, it is possible to build multiplexers-demultiplexers, which can be used either as multiplexers or as demultiplexers. Multiplexers-demultiplexers are designated by MX. Among the produced multiplexers-demultiplexers, we can highlight such as K564KP1, K590KP1. Multiplexers-demultiplexers are part of the K176, K561, K591, K1564 series.
A multiplexer can be used as a universal logic element (ULE) to implement logical functions.
In the ULE, each set of arguments corresponds to the transmission of one of the configuration signals to the output. If this signal is the value of a function on a given set of arguments, then the ULE implements the given function.
Different functions will have different setup codes.
The tuning alphabet is (0, 1) - tuning is carried out using the constants 0 and 1.
If the number of arguments exceeds the number of address inputs of the ULE, then it is necessary to expand the alphabet of tuning signals by transferring the arguments to the number of tuning signals.
Transferring one of the arguments to the number of setting signals allows you to implement functions with the number of arguments one more than when setting with constants.
You can go further along the path of expanding the alphabet of tuning signals. In this case, additional logic circuits will be needed that reproduce residual functions that will depend on more than one argument.
For example, if two arguments are converted into setting signals, then the additional logic circuits will be two-input.
Multiplexers,
demultiplexers
Using a multiplexer as a universal logic element for implementing logical functions
Multiplexers, demultiplexers
Demultiplexers
They perform the opposite function of a multiplexer - they transmit data from one input channel to one of several receiver channels.
The demultiplexer has one information input x, n information outputs, ..., and k control (address) inputs, ..., .
Usually, just like multiplexers, .
Multiplexers, demultiplexers
The binary code A, arriving at the address inputs, determines one of the n outputs, to which the value of the variable from the information input is transferred, i.e., the demultiplexer implements the following functions:
Multiplexers, demultiplexers
An example of a demultiplexer having
information outputs and address inputs,
Multiplexers,
demultiplexers
The demultiplexer function is easily implemented using a decoder if its EN permission input is used as the information input of the demultiplexer, and the decodable code inputs are used as address inputs. In this case, when the signal value at the EN input is active, the output corresponding to the code supplied to the address inputs is selected.
Therefore, DS ICs that have a permissive input, as noted earlier, are called
Multiplexers, demultiplexers
The term multiplexing
is the process of transmitting data from several sources over a common channel, and the device that performs the operation of combining data into one channel on the transmitting side is usually called
multiplexer.
Such a device is capable of temporarily separating signals coming from several
sources, and transmit them to the channel
(line) of communication one after another in
Multiplexers, demultiplexers
On the receiving side, you need to perform the reverse operation -
received via the communication channel at successive moments in time, at their receivers. This operation is performed demultiplexer.
The combined use of a multiplexer and a demultiplexer allows data transmission
Multiplexers,
demultiplexers
Combined use of a multiplexer and a demultiplexer to transmit data from n sources to n receivers over a common line
“Graphs of functions and their properties” - 7) The function is continuous on any interval of the form (?k; ? + ?k). Work orally: tg(- x) = - tg x. 2) Even or odd function. Describe the properties of the function y = ctgx. 6) The function has neither the largest nor the smallest values. The function y = tan x has neither a maximum nor a minimum value. D(f): the set of all real numbers except numbers of the form x = ?k.
“Mathematics of graphs” - How are graphs constructed? What can you draw with graphs? So, the purpose of the study. Let's get acquainted with wider applications: medicine, geodesy... What methods of constructing graphs do you know? Interesting. Graphs: difficult, work awaits you: Most naturally, functional dependencies are reflected using graphs.
“Graph of a function grade 7” - Compare numbers: Construct a graph of a function using the rules of movement: Determine the correspondence between the graph of a function and the formula: Dependent variable. Let's build a graph of a function by points: Examples leading to the concept of a function. Construct a graph of the function: Present the expressions as a monomial of the standard form:
“Inverse proportionality graph” - Even, odd. Continuity. Inverse proportionality. Hyperbola. Hyperbole and space satellites. Application of hyperboloids. Constructing an inverse proportionality graph. Axes of symmetry of a hyperbola. Inverse proportionality function. Hyperboloids of rotation. Domain. Asymptote.
“Graphing” - Build a graph of the function. Find all values of a for which Eq. Let's apply the generalized region method. We can easily read the answer from the picture. The original equation is equivalent to the set: By adding the corresponding coordinates, we obtain the desired graph. Let's build a graphical image of the correspondences included in the system.
“Graphing a function with a modulus” - Reinforced knowledge on previously studied functions. Y = x – 2. Question for the class. Generalization. Plotting function graphs. Y = sinx. Try to create graphs yourself. Y = lnx. Lesson of generalization and systematization of knowledge. Learned knowledge. Linear function. Y = f(x). Project activities. Y = x2 – 2x – 3.
Demultiplexers
Demultiplexer is a circuit that performs a function inverse to that of a multiplexer, i.e. this is a combinational circuit that has one information input (D), n information outputs (y0, y1, ..., yn-1) and k control (address) inputs (A0, A1, ..., Ak-1). Typically, just like multiplexers, 2k= n. The binary code arriving at the address inputs determines one of the n outputs, to which the variable value from the information input (D) is transferred, i.e. The demultiplexer implements the following functions:
The table of operation of a demultiplexer having n = 4 information outputs (y0, y1, y2, y3) and k = 2 address inputs (A0, A1) is presented in table. 1.2.
Table 1.2
Equations describing the operation of the demultiplexer:
The demultiplexer circuit built according to these equations and its graphical representation are presented in Fig. 1.3.
Rice. 1.3 - Diagram of the demultiplexer “1-4” (a) and its symbolic image (b)
The demultiplexer function is easily implemented using a decoder if its “Resolution” (E) input is used as the information input of the demultiplexer, and inputs 1, 2, 4 ... are used as address inputs of the demultiplexer A0, A1, A2, ... Indeed, with an active signal value at input E, the output corresponding to the code supplied to the address inputs is selected. Therefore, decoder ICs that have an enabling input are sometimes called not just decoders, but decoder-demultiplexers (for example, K155ID4, K531ID7, etc.).
Application of multiplexers and demultiplexers
The term “multiplexing” refers to the process of transmitting data from several sources over a common channel, and a device that performs the operation of combining data into one channel on the transmitting side is usually called a multiplexer. Such a device is capable of temporarily separating signals coming from several sources and transmitting them to a communication channel (line) one after another in accordance with the change of codes at its address inputs.
On the receiving side, it is usually necessary to perform the reverse operation - demultiplexing, i.e. distribution of pieces of data received via a communication channel at successive moments in time among their receivers. This operation is performed by a demultiplexer. The combined use of a multiplexer and a demultiplexer to transmit data from n sources to n receivers over a common line is illustrated in Fig. 1.4. (In general, the number of data sources is not equal to the number of receivers.)
Rice. 1.4
If in the circuit (Fig. 1.4) n different sources and receivers are replaced with n-bit sources and receivers, for example, RGist registers. and RGpr. (shown as dotted lines), the circuit can be used to convert n-bit parallel code on the transmit side to serial code (using a multiplexer) and serial code to parallel code on the receiving side (using a demultiplexer).
When using a multiplexer and demultiplexer in this way, the output signals of a binary counter are used as their address codes, which sequentially generates binary codes of numbers from 0 to n-1 at its outputs.
A multiplexer can be used as a universal logical element to implement any logical function from a number of arguments equal to the number of address inputs of the multiplexer. Let's show this using the example of a logical function defined by its truth table (Table 1.3).
We select a multiplexer that has three address inputs (according to the number of function arguments) and eight information inputs.
Rice. 1.5
To implement the given function, we connect the information inputs of the multiplexer to the logical levels “1” and “0” in a sequence that completely copies the sequence of ones and zeros of the function in the truth table (Fig. 1.5). In this case, neither recording of SDNF nor its minimization is required. By the way, the function given in table. 1.3 (parity of the number of ones in a three-bit word) is not simplified, therefore, for its implementation, for example, in the basis of the “NAND” LE, it requires four “3I-NOT” LEs and three inverters, i.e. a total of three ICs will be required. At the same time, to implement the scheme according to Fig. 1.5 requires only one “8-1” multiplexer IC. For this reason, the method of implementing functions of three or more arguments using IC multiplexers is very popular among developers.
Multiplexers and demultiplexers (mux and demux in English abbreviation) are fairly common components in digital electronics. Understanding the logical processes occurring in them will allow us to better understand the circuits with their participation and develop more complex electronic devices
Multiplexers and demultiplexers work opposite to each other, but according to the same principle. They consist of information inputs, information outputs and a switch (selector).
The image below shows a schematic representation of a multiplexer and a demultiplexer.
The multiplexer has several information inputs. The multiplexer switch selects which of these inputs should be used and connects it to the information output, of which the multiplexer has only one. This situation can be compared to if a bunch of people would like to tell you something of their own, but you can only listen to one at a time.
A demultiplexer, on the contrary, has only one information input, and the switch connects it to one information output at a time. That is, it is the same as if you want to say something to a crowd of people, but at any given time you can only say it to one person from this crowd.
There are also microcircuits that combine the functions of multiplexers and demultiplexers. In English they are usually designated mux/demux. They can also be called bidirectional multiplexers or simply switches. They allow the signal to be transmitted in both directions. So not only can you talk to someone, but someone in the crowd can talk to you at a certain point in time.
In this case, the internal switch usually has several information inputs that are addressed in binary form. Almost all such microcircuits have an OE line (output enable or output is active). There is also a demultiplexer inside the chip with one input and usually four outputs. To select an output, the microcircuit also has two lines for addressing the output (00, 01, 10, 11).
There are both digital and analog multiplexers. Digital switches are logical switches whose output voltage will be the same as the supply voltage. Analog ones connect the voltage of the selected input to the output.
The principle of multiplexing and demultiplexing was used at the dawn of the development of telephony at the beginning of the last century. Then the person who wanted to call his friend picked up the phone and waited for the operator to answer. This is a multiplexer part, since at a certain point in time the operator selects from among the set the line on which this person “sits”. The person says that he wants to talk to a friend whose number is 12345. This is the switchboard part, here the operator receives the number (address). Next, he connects the connector to his friend’s channel. This is the demultiplexer part. Here one line from many channels connects to only one.
Multiplexers and demultiplexers will help you solve the problem of expanding the number of input or output lines if the number of GPIOs of your microcontroller is too small. If your project includes many sensors, then you can connect them to a multiplexer. The output of the multiplexer then needs to be connected to the ADC and, by switching the addresses of the lines, sequentially read data from the sensors.
Multiplexers are also useful when you have several I2C interface chips that have the same address. Simply connect the SDA/SCL lines to the switch and control them in series. Multiplexers and demultiplexers can also be used as level converters.
