Diode logic elements or, and. Diode gates or, and Logic 2

A typical diagram of an integrated element of emitter-coupled logic is shown in fig. 2.15.

rice. 2.15.

Transistors VT 0, VT 1, VT 2, VT 3 work in the current switch circuit, transistors VT 4, VT 5 - in the output emitter followers. The diagram shows the values ​​of the potentials at various points when a voltage of log.1 level is applied to the input; the values ​​of the potentials of the same points are enclosed in brackets for the case when voltages of the log.0 level are applied to all inputs of the element. The values ​​of these potentials correspond to the following levels:

· power supply voltage E to = 5 V;

· level log.1 U 1 = 4.3 V;

· level log.1 U 0 = 3.5 V;

· the voltage between the base and the emitter of an open transistor U be \u003d 0.7 V.

Let's consider the principle of operation of the ESL integral logic element (see Fig. 2.15).

Let voltage U 1 = 4.3 V be applied to Vx 1. Transistor VT 1 is open; the emitter current of this transistor creates a voltage drop across the resistor R U a = U 1 -U be = 4.3 - 0.7 = 3.6 V; the collector current creates a voltage U Rk1 = 0.8 V on the resistor R k1; voltage at the collector of the transistor U b \u003d E k - U Rk1 \u003d 5 - 0.8 \u003d 4.2 V.

The voltage between the base and emitter of the transistor VT 0 U be VT0 \u003d U - U a \u003d 3.9 - 3.6 \u003d 0.3 V; this voltage is not enough to open the transistor VT 0. Thus, the open state of any of the transistors VT 1 , VT 2 , VT 3 leads to the closed state of the transistor VT 0 . The current through the resistor R k2 is very small (only the base current of the transistor VT 5 flows) and the voltage on the collector VT 0.

Consider another state of the logic element. Let the voltage log.0 U 0 \u003d 3.5 V operate at all inputs. In this case, the transistor VT 0 turns out to be open (of all the transistors whose emitters are combined, the one on the basis of which a higher voltage opens); U a \u003d U - U be \u003d 3.9 - 0.7 \u003d 3.2 V; the voltage between the base and emitter of transistors VT 1, VT 2, VT 3 is equal to U be VT1 ... VT0 \u003d U 0 - U a \u003d 3.5 - 0.7 \u003d 0.3 V and these transistors are closed; U b = 5 V; U in \u003d 4.2 V.

Voltages from points b and c are transmitted to the outputs of the element through emitter repeaters; in this case, the voltage level decreases by the value U be \u003d 0.7 V. Let us pay attention to the important circumstance that the voltages at the outputs are equal to U 1 (4.3 V) or U 0 (3.5 V).

Let's find out what logical function is formed at the outputs of the element.

At the point in and at Out 2, a low-level voltage is formed when the transistor VT 0 is open, i.e. in the case when x 1 \u003d 0, x 2 \u003d 0, x 3 \u003d 0. For any other combination of values ​​​​of input variables, the transistor VT 0 is closed and a high level voltage is generated at Output 2. It follows from this that a disjunction of variables x 1 Vx 1 Vx 1 is formed on the output 2 . At Out 1, the OR-NOT function is formed.

Therefore, the logical element performs the OR-NOT and OR operations.

In ESL microcircuits, point d is made common, and point d is connected to a power source with a voltage of -5V. In this case, the potentials of all points of the circuit are reduced to 5 V.

The considered logical element belongs to the class of the fastest elements (short signal propagation delay time) is provided by the following factors: open transistors are in active mode (not in saturation mode); the use of emitter followers at the outputs accelerates the process of recharging the capacitances connected to the outputs; transistors are connected according to the switching circuit with a common base, which improves the frequency properties of transistors and speeds up the process of their switching; a small difference in logical levels U 1 -U 0 = 0.8 V is selected (however, this leads to a relatively low noise immunity of the element).

Logic elements on MIS transistors

rice. 2.16

On fig. 2.16 shows a diagram of a logic element with an induced channel of type n (the so-called n MIS technology). The main transistors VT 1 and VT 2 are connected in series, the transistor VT 3 acts as a load. In the case when a high voltage U 1 acts on both inputs of the element (x 1 \u003d 1, x 2 \u003d 1), both transistors VT 1 and VT 2 turn out to be open and a low voltage U 0 is set at the output. In all other cases, at least one of the transistors VT 1 or VT 2 is closed and the voltage U 1 is set at the output. Thus, the element performs a logical NAND function.

rice. 2.17

On fig. 2.17 shows a diagram of an OR-NOT element. A low voltage U 0 is set at its output, if at least one of the inputs has a high voltage U 1, which opens one of the main transistors VT 1 and VT 2.

rice. 2.18

Shown in fig. 2.18 the circuit is a circuit of the OR-NOT element of the CMOS technology. In it, transistors VT 1 and VT 2 are the main ones, transistors VT 3 and VT 4 are load ones. Let the high voltage be U 1 . In this case, the transistor VT 2 is open, the transistor VT 4 is closed, and regardless of the voltage level at the other input and the state of the remaining transistors, a low voltage U 0 is set at the output. The element implements a logical OR-NOT operation.

The CMTD circuit is characterized by a very low current consumption (and, consequently, power) from power sources.

Logic elements of integral injection logic

rice. 2.19

On fig. 2.19 shows the topology of the logic element of the integral injection logic (I 2 L). To create such a structure, two phases of diffusion in silicon with n-type conductivity are required: during the first phase, regions p 1 and p 2 are formed, the second phase - regions n 2 .

The element has the structure p 1 -n 1 -p 2 -n 1 . It is convenient to consider such a four-layer structure, representing it as a connection of two conventional three-layer transistor structures:

p 1 - n 1 - p 2 n 1 - p 2 - n 1

The scheme corresponding to such a representation is shown in Fig. 2.20, a. Consider the operation of the element according to this scheme.

rice. 2.20

Transistor VT 2 with a structure of the type n 1 -p 2 -n 1 performs the functions of an inverter with several outputs (each collector forms a separate output of the element according to the open collector circuit).

Transistor VT 2, called injector, has a structure like p 1 -n 1 -p 2 . Since the area n 1 for these transistors is common, the emitter of the transistor VT 2 must be connected to the base of the transistor VT 1; the presence of a common area p 2 leads to the need to connect the base of the transistor VT 2 with the collector of the transistor VT 1 . This is how the connection of transistors VT 1 and VT 2 is formed, shown in Fig. 2.20, a.

Since a positive potential acts on the emitter of the transistor VT 1, and the base is at zero potential, the emitter junction is forward-biased and the transistor is open.

The collector current of this transistor can close either through the transistor VT 3 (inverter of the previous element), or through the emitter junction of the transistor VT 2.

If the previous logical element is in the open state (transistor VT 3 is open), then at the input of this element a low voltage level, which, acting on the basis of VT 2, keeps this transistor in the closed state. The current of the injector VT 1 closes through the transistor VT 3. When the previous logic element is closed (transistor VT 3 is closed), the collector current of the injector VT 1 flows into the base of the transistor VT 2, and this transistor is set to the open state.

Thus, when VT 3 is closed, the transistor VT 2 is open and, conversely, when VT 3 is open, the transistor VT 2 is closed. The open state of the element corresponds to the state log.0, the closed state corresponds to the state log.1.

The injector is a constant current source (which may be common to a group of elements). Often use the conditional graphic designation of the element, shown in Fig. 2.21b.

On fig. 2.21a shows a circuit that implements the OR-NOT operation. The connection of the collectors of elements corresponds to the operation of the so-called mounting AND. Indeed, it is enough that at least one of the elements is in the open state (log.0 state), then the injector current of the next element will be closed through the open inverter and a low level of log.0 will be set at the combined output of the elements. Therefore, at this output, a value corresponding to the logical expression x 1 x 2 is formed. Applying the de Morgan transform to it leads to the expression x 1 x 2 = . Therefore, this connection of elements really implements the OR-NOT operation.

rice. 2.21

Logical elements AND 2 L have the following advantages:

· provide a high degree of integration; in the manufacture of I 2 L circuits, the same technological processes are used as in the manufacture of integrated circuits on bipolar transistors, but the number of technological operations and the necessary photomasks is less;

· low voltage is used (about 1V);

· provide the possibility of exchanging power for speed over a wide range (you can change the power consumption by several orders of magnitude, which will accordingly lead to a change in speed);

· are in good agreement with TTL elements.

On fig. 2.21b shows the transition scheme from the elements AND 2 L to the TTL element.

In digital circuitry, a digital signal is a signal that can take on two values, considered as a logical "1" and a logical "0".

Logic circuits are implemented on logical elements: "NOT", "AND", "OR", "AND-NOT", "OR-NOT", "XOR" and "Equivalence". The first three logical elements allow you to implement any arbitrarily complex logical function in a boolean basis. We will solve problems for logic circuits implemented in the Boolean basis.

Several standards are used to designate logic elements. The most common are American (ANSI), European (DIN), international (IEC) and Russian (GOST). The figure below shows the designations of logical elements in these standards (to enlarge, you can click on the picture with the left mouse button).

In this lesson, we will solve problems for logic circuits, in which logic elements are designated in the GOST standard.

Tasks for logic circuits are of two types: the problem of synthesizing logic circuits and the problem of analyzing logic circuits. We will start with the second type of problem, since in this order it is possible to quickly learn how to read logic diagrams.

Most often, in connection with the construction of logical circuits, the functions of the algebra of logic are considered:

• three variables (to be considered in the problems of analysis and in one problem of synthesis);
• four variables (in synthesis problems, that is, in the last two paragraphs).

Consider the construction (synthesis) of logical circuits

• in the boolean basis "AND", "OR", "NOT" (in the penultimate paragraph);
• in the also common bases "AND-NOT" and "OR-NOT" (in the last paragraph).

The task of analyzing logic circuits

The task of analysis is to determine the function f implemented by a given logic circuit. When solving such a problem, it is convenient to follow the following sequence of actions.

1. The logical scheme is divided into tiers. Tiers are assigned sequential numbers.
2. The outputs of each logical element are indicated by the name of the desired function, provided with a digital index, where the first digit is the tier number, and the remaining digits are the ordinal number of the element in the tier.
3. For each element, an analytical expression is written that relates its output function to the input variables. The expression is defined by the logical function implemented by the given logical element.
4. Substitution of some output functions through others is performed until a Boolean function is obtained, expressed through input variables.

Example 1

Solution. We divide the logic circuit into tiers, which is already shown in the figure. Let's write down all the functions, starting from the 1st tier:

x, y, z :

Example 2 Find the boolean function of the logic circuit and make a truth table for the logic circuit.

Example 3 Find the boolean function of the logic circuit and make a truth table for the logic circuit.

We continue to search for the boolean function of the logic circuit together

Example 4 Find the boolean function of the logic circuit and make a truth table for the logic circuit.

Solution. We break the logic circuit into tiers. Let's write down all the functions, starting from the 1st tier:

Now let's write all the functions, substituting the input variables x, y, z :

As a result, we get the function that the logic circuit implements at the output:

.

Truth table for a given logic circuit:

Example 5 Find the boolean function of the logic circuit and make a truth table for the logic circuit.

Solution. We break the logic circuit into tiers. The structure of this logic circuit, unlike the previous examples, has 5 tiers, not 4. But one input variable - the lowest one - runs through all the tiers and directly enters the logic element in the first tier. Let's write down all the functions, starting from the 1st tier:

Now let's write all the functions, substituting the input variables x, y, z :

As a result, we get the function that the logic circuit implements at the output:

.

Truth table for a given logic circuit:

The problem of synthesizing logic circuits in a Boolean basis

The development of a logical circuit according to its analytical description is called the problem of synthesis of a logical circuit.

Each disjunction (logical sum) corresponds to the "OR" element, the number of inputs of which is determined by the number of variables in the disjunction. Each conjunction (logical product) corresponds to the "AND" element, the number of inputs of which is determined by the number of variables in the conjunction. Each negation (inversion) corresponds to the element "NOT".

Often the design of a logic circuit begins with the definition of a logic function that the logic circuit must implement. In this case, only the truth table of the logic circuit is given. We will analyze just such an example, that is, we will solve a problem that is completely inverse to the problem of analyzing logic circuits considered above.

Example 6 Construct a logic circuit that implements a function with a given truth table:

Solution. We analyze the truth table for the logic circuit. We define a function that will be obtained at the output of the circuit and intermediate functions that take arguments at the input x And y. In the first line, the result of the implementation of the output function, given that the values ​​of the input variables are equal to one, should be a logical "0", in the second line - with different values ​​of the input variables, the output should also be a logical "0". Therefore, it is necessary that the output function be a conjunction (logical product).

Just like standard Boolean expressions, information at the inputs and outputs of various logic elements or logic circuits can be collected in a single table - a truth table.

truth table gives a visual representation of the system of logical functions. The truth table displays the signals at the outputs of logic elements for all possible combinations of signals at their inputs.

As an example, consider a logic circuit with two inputs and one output. Let's mark the input signals as "A" and "B", and the output as "Q". There are four (2²) possible combinations of input signals that can be applied to these two inputs ("ON - signal present" and "OFF - signal absent").

However, when it comes to logical expressions and, especially, the truth table of logical elements, instead of the general concept of "signal presence" and "signal absence", bit values ​​are used, which represent the logic level "1" and the logic level "0", respectively.

Then four possible combinations of "A" and "B" for a 2-input logic element can be represented as follows:

1. "OFF" - "OFF" or (0, 0)
2. "OFF" - "ON" or (0, 1)
3. "ON" - "OFF" or (1, 0)
4. "ON" - "ON" or (1, 1)

Therefore, a logic circuit with three inputs will have eight possible combinations (2³) and so on. To ensure an easy understanding of the essence of the truth table, we will study it only on simple logic elements with the number of inputs not exceeding two. But, despite this, the principle of obtaining logical results for multi-input circuit elements remains the same.

In practice, the truth table consists of one column for each of the input variables (eg A and B), and one last column for all possible outcomes of the logical operation (Q). Therefore, each row of the truth table contains one of the possible input variables (for example, A = 1, B = 0), and the result of the operation with these values.

truth table

Element "And"

For the logical element "AND", the output Q will contain log.1 only if both inputs ("A" and "B") are given a signal log.1

Microcircuits containing the logical element "AND":

• K155LI1, analogue of SN7408N
• K155LI5 with open collector, similar to SN74451N
• K555LI1, analogue of SN74LS08N
• K555LI2 with open collector, similar to SN74LS09N

OR element

The output of Q, the “OR” element, will have a log.1 if any of the two inputs or both inputs are immediately logged.1

Microcircuits containing the logic element "OR":

• K155LL1, analogue of SN7432N
• K155LL2 with open collector, similar to SN75453N
• K555LL1, analogue of SN74LS32N

Element "NOT"

In this case, the output of Q, the logical element "NOT", will have a signal opposite to the input signal.

Microcircuits containing a logical element "NOT":

• K155LN1, similar to SN7404N
• K155LN2 with open collector, similar to SN7405N
• K155LN3, similar to SN7406N
• K155LN5 with open collector, similar to SN7416N
• K155LN6, analogue of SN7466N

Element "AND-NOT"

The output Q of the "AND-NOT" element will be log.1 if there is no log.1 signal at both inputs at the same time

Microcircuits containing a logical element "AND-NOT":

• K155LA3, similar to SN7400N
• K155LA8, similar to SN7401N
• K155LA9 with open collector, similar to SN7403N
• K155LA11 with open collector, similar to SN7426N
• K155LA12 with open collector, similar to SN7437N
• K155LA13 with open collector, similar to SN7438N
• K155LA18 with open collector, similar to SN75452N

OR-NOT element

Only if we apply log.0 to both inputs of the OR-NOT logic element, we will get the corresponding log.1 signal at its output Q

Microcircuits containing the logical element "OR-NOT":

• K155LE1, analogue of SN7402N
• K155LE5, similar to SN7428N
• K155LE6, similar to SN74128N

XOR element

In this case, the output Q will contain log.1 if two opposite signals are applied to the input of the XOR element.

Microcircuits containing the logical element "XOR":

• K155LP5, similar to SN7486N

Let's summarize by collecting all the previously obtained results of the work of logical elements in a single truth table:

Any digital microcircuits are built on the basis of the simplest logic elements:

Consider the design and operation of digital logic elements in more detail.

inverter

The simplest logic element is the inverter, which simply changes the input signal to the exact opposite value. It is written in the following form:

where the line over the input value and denotes its change to the opposite. The same action can be written with the help given in table 1. Since the inverter has only one input, its truth table consists of only two lines.

Table 1. Inverter gate truth table

As a logical inverter, you can use the simplest amplifier with a transistor switched on (or a source for a field effect transistor). The schematic diagram of the inverter logic element, made on a bipolar n-p-n transistor, is shown in Figure 1.

Logic inverter chips can have different signal propagation times and can operate on different types of loads. They can be performed on one or several transistors. The most common logic elements are made by TTL, ESL and CMOS technologies. But regardless of the logic element scheme and its parameters, they all perform the same function.

In order for the features of switching on transistors not to obscure the function performed, special designations for logical elements were introduced - conditional graphic designations. inverter is shown in Figure 2.

Inverters are present in almost all series of digital microcircuits. In domestic microcircuits, inverters are designated by the letters LN. For example, the 1533LN1 chip contains 6 inverters. Foreign microcircuits to indicate the type of microcircuit, a digital designation is used. An example of an IC containing inverters is the 74ALS04. The name of the microcircuit reflects that it is compatible with TTL microcircuits (74), produced according to improved low-power Schottky technology (ALS), contains inverters (04).

Currently, surface-mounted microcircuits (SMD microcircuits) are more often used, which contain one logical element each, in particular an inverter. An example is the SN74LVC1G04 chip. The microcircuit is manufactured by Texas Instruments (SN), is compatible with TTL microcircuits (74) is produced according to low-voltage CMOS technology (LVC), contains only one logic element (1G), it is an inverter (04).

To study the inverting logic element, you can use widely available electronic elements. So, as an input signal generator, you can use ordinary switches or toggle switches. To study the truth table, you can even use a regular wire, which we will alternately connect to a power source or a common wire. As a logic probe, a low-voltage light bulb or LED connected in series with a current-limiting one can be used. A schematic diagram of the study of the logic element of the inverter, implemented using these simple electronic elements, is shown in Figure 3.

The scheme for studying a digital logic element, shown in Figure 3, allows you to visually obtain data for the truth table. A similar study is carried out in More complete characteristics of the digital inverter logic element, such as the delay time of the input signal, the rate of rise and fall of the signal edges at the output, can be obtained using a pulse generator and an oscilloscope (preferably a two-channel oscilloscope).

Logic element "AND"

The next simplest logical element is a circuit that implements the operation of logical multiplication "AND":

where the symbol ^ and denotes the logical multiplication function. Sometimes the same function is written in a different form:

The same action can be written using the truth table shown in Table 2. The formula above uses two arguments. Therefore, the logic element that performs this function has two inputs. It is designated "2I". For the logical element "2I" the truth table will consist of four rows (2 2 = 4) .

Table 2. Truth table of the logical element "2I"

As can be seen from the above truth table, an active signal at the output of this logic element appears only when there are ones at both the X and Y inputs. That is, this logical element actually implements the "AND" operation.

The easiest way to understand how the 2I logic element works is with a circuit built on idealized electronically controlled keys, as shown in Figure 2. In the above circuit diagram, current will flow only when both keys are closed, which means that a unit level at its output will appear only with two units at the input.

The conditional-graphic representation of the circuit that performs the logical function "2I" on the circuit diagrams is shown in Figure 3, and from now on, the circuits that perform the "AND" function will be shown in this form. This image does not depend on the specific circuit diagram of the device that implements the logical multiplication function.

The function of the logical multiplication of three variables is described in the same way:

Its truth table will already contain eight rows (2 3 = 4). The truth table of the three-input logical multiplication circuit "3I" is shown in Table 3, and the conditional graphic image is in Figure 4. In the circuit of the logical element "3I", built according to the principle of the circuit shown in Figure 2, you will have to add a third key.

Table 3. Truth table of the circuit that performs the logical function "3I"

You can get a similar truth table using the 3I logic element research circuit, similar to the logic inverter research circuit shown in Figure 3.

Logic element "OR"

The next simplest logical element is a circuit that implements the logical addition operation "OR":

where the symbol V denotes the logical addition function. Sometimes the same function is written in a different form:

The same action can be written using the truth table given in Table 4. The formula above uses two arguments. Therefore, the logic element that performs this function has two inputs. Such an element is designated "2OR". For the element "2OR" the truth table will consist of four rows (2 2 = 4).

Table 4. Truth table of the logic element "2OR"

As in the case considered for , we will use the keys to implement the "2OR" scheme. This time we will connect the keys in parallel. The circuit that implements the truth table 4 is shown in Figure 5. As can be seen from the above circuit, the level of a logical unit will appear at its output as soon as any of the keys is closed, that is, the circuit implements the truth table shown in Table 4.

Since the function of logical summation can be implemented by various circuit diagrams, the special symbol "1" is used to designate this function on the circuit diagrams, as shown in Figure 6.

Date of the last update of the file 29.03.2018

Literature:

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