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Дома > Other > Exploring NAND, AND, NOR, OR Gate: A Deep Dive into Basic Logic Gates

Exploring NAND, AND, NOR, OR Gate: A Deep Dive into Basic Logic Gates

Время обновления: 2023-11-24 14:35:49

Contents

Logic gates are the fundamental components of all digital circuits in digital electronics, functioning as switching devices. A logic gate is a digital circuit that executes various logical operations in a digital device or system. These gates are responsible for carrying out essential logical functions that form the foundation of digital circuits. Virtually every electronic device utilized in contemporary times incorporates some variation of logic gates in its design. This article provides an overview of the NAND, AND, NOR, OR gates, these four basic logic gates, and explores what are the universal gates.


What is Logic Gate?


A logic gate functions as a foundational element in digital circuits. These gates make decisions within a circuit based on the digital signals received from their inputs. Typically, logic gates feature two inputs and one output. Their operation is rooted in Boolean algebra, where each terminal exists in either binary states: false (0) or true (1). The binary output varies depending on the specific logic gate type and input combinations. Analogous to a light switch, a logic gate has an off position (0) and an on position (1). Integrated circuits (IC) commonly incorporate logic gates.


NAND Gate


NAND is an acronym for NOT-AND. In digital logic, a NAND gate is essentially an AND gate accompanied by a NOT circuit, resulting in a negated output. This combination stands out as one of the most valuable configurations of logic gates.


Circuit


The following is an electromechanical circuit illustrating the principle of a NAND gate.


An electromechanical NAND circuit.png


The battery powers the LED via the typically closed switches a and b. Solenoid R1 governs switch a, while solenoid R2 controls switch b.


Initially, inputs A and B are without power, signifying a logic 0 signal (assuming positive logic). The LED is illuminated in this state, and Y = 1 (logic 1).


When only input A is connected to the battery (logic 1), solenoid R1 opens switch a. Despite this, the LED receives power through switch b, maintaining Y = 1 (logic 1).


Similarly, when only input B is connected to the battery (logic 1), solenoid R2 opens switch b. Nevertheless, the LED still receives power through switch a, and Y = 1 (logic 1).


Ultimately, when both inputs, A and B, are connected (logic 1), solenoids R1 and R2 open switches a and b, leading to the de-energization of the LED. The LED is extinguished in this state, and Y = 0 (logic 0).


Truth Table


Compiles this data into a truth table.


ABY
001
011
101
110

The truth table for a two-input NAND circuit


Logic Symbol and Boolean Expression


Displays the circuit symbol and Boolean expression for a two-input NAND gate.


Two-input NAND gate symbol and Boolean expression.png


For a NAND gate with more than two inputs, the Boolean expression is expressed as

Boolean expression for a NAND gate.png


Using a Combination of NAND Gates to Create Other Basic Logic Gates


The exclusive use of the NAND circuit allows for the implementing various logical functions. Several instances are detailed below.


In Figure 1, a two-input NAND gate is configured to function as a NOT circuit. It is noteworthy that a single-input NAND gate inherently acts as a NOT.


A NOT circuit made with a two-input NAND gate.png

Figure 1. A NOT circuit made with a two-input NAND gate


Moving to Figure 2, two NAND gates are interconnected to form a two-input AND gate.


A two-input AND gate made with two NAND gates.png

Figure 2. A two-input AND gate made with two NAND gates


Lastly, Figure 3 illustrates the arrangement of three NAND gates to construct a two-input OR gate.


A two-input OR gate made with three NAND gates.png

Figure 3. A two-input OR gate made with three NAND gates


Applications


NAND gates find diverse practical applications in real-world scenarios, and a selection of these applications is elucidated below:


  • Integration into alarm circuits for light-induced radiation detection.

  • Utilization of freezer warning buzzer systems.

  • Deployment in automatic temperature regulation circuits, employing NAND logic gates.

  • Analysis of sensor status connected to different doors and windows.

  • Incorporation into burglar alarm systems.


NAND Gate IC


The prevalent integrated circuits (ICs) featuring NAND gates include:


In TTL logic:


  • 74LS00 - Quad 2-input NAND IC

  • 74LS10 - Triple 3-input NAND IC

  • 74LS20 - Dual 4-input NAND IC

  • 74LS30 - Single 8-input NAND IC


In CMOS logic:


  • CD4011 - Quad 2-input NAND IC

  • CD4023 - Triple 3-input NAND IC

  • CD4012 - Dual 4-input NAND IC


AND Gate


An AND gate is a logical circuit with one output and two or more inputs. It follows the principles of logical multiplication, where the output is low if any input is low (0). Conversely, when all inputs are high (1), the output is also high. Although an AND gate can accommodate various inputs, the 2-input and 3-input configurations are the most prevalent.


Circuit


AND Gate Diode Circuit Diagram


Typically, an AND gate is crafted using either diodes or transistors.


When diodes are employed in the design of an AND gate, it is termed a diode AND gate. The fundamental circuit of a diode AND gate is illustrated below.


basic circuit of a diode AND gate-1.png


In this diode circuit, +5V is initially applied at point C. Subsequently, applying +5V at both A and B results in the reversal bias of both diodes, rendering them in an OFF or open circuit state.


basic circuit of a diode AND gate-2.png


Under these circumstances, with both diodes OFF, no current flows through resistor R, causing the voltage at point X to mirror the +5V at point C. Consequently, the circuit output is recognized as high or logical 1.


basic circuit of a diode AND gate-3.png


Conversely, if either point A, point B, or both are set at 0 Volts or grounded, the corresponding diode becomes forward-biased, assuming an 'ON' or short-circuited status. This allows the +5V supply at point C to find a path to ground through either diodes.


As the current traverses from C to ground via resistor R, the entire 5V experiences a drop across the resistor, consequently, the voltage at point X becomes low or logically zero.


While diodes in the forward-biased state do not emulate an ideal short circuit, a discernible voltage drop, equivalent to the forward bias voltage, occurs. This voltage drop, present at point X during low output conditions, results in a practical low output ranging from 0.6 to 0.7V, which is conventionally considered zero.


basic circuit of a diode AND gate-4.png


AND Gate Transistor Circuit Diagram


An AND logic gate can also be implemented through a transistor AND gate. The circuit diagram for a transistor AND gate is depicted below:


transistor circuit diagram for an AND gate-1.png


In this circuit, when A, B, or both A and B are grounded or set at 0V potential, transistors T1, T2, or both T1 and T2 are in the OFF state.


This condition arises because terminals A and B are the base terminals for transistors T1 and T2, respectively. An absence of base voltage renders a transistor OFF. With the paths through T1 and T2 being open-circuited, there is sufficient potential to turn on transistor T3.


Consequently, current flows from the supply to the ground through T3. This results in the entire supply voltage dropping across R1, causing the potential at terminal X to become low or logically zero.


transistor circuit diagram for an AND gate-2.png


If either of the transistors T1 and T2 is OFF, the same output (low potential at X) is observed since both transistors are in series.


Next, let's examine the logical value of X when both A and B are set to a high logical value. Applying +5V to both A and B, i.e., at the base of transistors T1 and T2, activates both transistors.


This activation causes the supply voltage to drop across R, and the base potential of transistor T3 becomes zero, leading to T3 turning OFF. Consequently, the supply voltage of +5V appears at X, which is logically 1 or higher.


transistor circuit diagram for an AND gate-3.png


Truth Table


The Truth Table of a 2-input AND Gate


ABC
000
010
100
111


The Truth Table of a 3-input AND Gate


ABCX
0000
0010
0100
0110
1000
1010
1100
1111


Logic Symbol and Boolean Expression


2-input AND Gate


The symbolic representation of a two-input AND gate is logically denoted as follows:


symbol for a two-input AND gate.png


Here, A and B symbolize the inputs of the gate, and X signifies the output. Logically, A, B, and X can each assume 0 (low) or 1 (high) values.


The boolean expression of the AND gate is succinctly expressed as:


AB=X


3-input AND Gate


In the case of three inputs rather than two, both the logical symbol and the truth table of the AND gate undergo modification.


The logical symbol for a 3-input AND gate is depicted as:


logical symbol of a 3-input AND gate.png


The boolean expression of the AND gate is succinctly expressed as:


ABC=X


Applications


  • The principal application of the AND gate lies in the realms of digital electronics and data transmission, where it facilitates the control of data passage through a channel.

  • Employed in digital measuring devices.

  • Utilized in alarm circuits.

  • Another application worth noting is the Inhibit gate, which operates contrary to the enabling gate.

  • Found in automatic temperature-regulating circuits.

  • Integrated into freezer warning buzzer devices.


AND gate IC


The prevalent integrated circuits (ICs) featuring AND gates include:


In TTL Logic:



In CMOS Logic:



NOR Gate


The NOR gate in digital logic is formed by combining an OR gate and an inverter or NOT gate in series. This inclusive NOR (Not-OR) gate typically maintains an output at logic level "1" but transitions to logic level "0" only when ANY of its inputs reach logic level "1". The Logic NOR Gate represents the inverse or "Complementary" counterpart of the inclusive OR gate discussed earlier.


Circuit


It's an electromechanical circuit illustrating the NOR gate principle.


An electromechanical NOR circuit.png


The battery powers the LED through normally closed switches a and b. Solenoid R1 governs switch a, while solenoid R2 controls switch b.


Initially, inputs A and B are without power, representing a logic 0 signal (assuming positive logic). The LED is illuminated in this state, and Y = 1 (logic 1).


By connecting only input A to the battery (logic 1), solenoid R1 opens switch a, interrupting the current and turning off the LED. In this scenario, Y = 0 (logic 0).


Similarly, connecting only input B to the battery (logic 1) has solenoid R2 open switch b, interrupting the current and turning off the LED. In this case, Y = 0 (logic 0).


Finally, connecting inputs A and B (logic 1) results in solenoids R1 and R2 opening switches a and b, de-energizing the LED. Under this condition, the LED is off, and Y = 0 (logic 0).


Truth Table


Summarizing these outcomes in a truth table:


ABY
001
010
100
110

The truth table for a two-input NOR circuit


The output of a NOR gate registers a logic 1 exclusively when all its inputs assume a logic 0. In all other combinations of inputs, the result is a logic 0.


Logic Symbol and Boolean Expression


It illustrates the logic symbol and Boolean expression for the NOR gate.


Two-input NOR gate symbol and Boolean expression.png


Using a Combination of NOR Gates to Create Other Basic Logic Gates


The entirety of logical operations can be achieved by exclusively utilizing the NOR circuit. Illustrated below are a few instances.


In Figure 4, a two-input NOR gate is configured to generate a NOT circuit. Notably, a single-input NOR gate inherently functions as a NOT.


A NOT circuit made with a two-input NOR gate figure 4.png

Figure 4. A NOT circuit made with a two-input NOR gate


Moving to Figure 5, two NOR gates are interconnected to form a two-input OR gate.


A two-input OR gate made with two NOR gates figure 5.png

Figure 5. A two-input OR gate made with two NOR gates


Lastly, Figure 6 exemplifies the interconnection of three NOR gates to construct a two-input AND gate.


A two-input AND gate made with three NOR gates figure 6.png

Figure 6. A two-input AND gate made with three NOR gates


Applications


  • Electronic devices

  • Alarm systems

  • Industrial automation

  • Digital circuit design

  • Traffic light systems

  • Data storage

  • Robotics

  • Medical devices

  • Home automation

  • Communication systems

  • Logic in calculators and computer keyboards

  • Power management

  • Aerospace applications

  • Gaming consoles

  • Automotive systems


NOR Gate IC


The prevalent integrated circuits (ICs) featuring NOR gates include:


In TTL Logic:



In CMOS Logic:


  • CD4001 Quad 2-input

  • CD4025 Triple 3-input

  • CD4002 Dual 4-input


OR Gate


The Logic OR Gate represents a digital logic circuit wherein the output assumes a HIGH state, i.e., logic level 1, solely when one or more of its inputs are in a HIGH state.


The output, Q, from a "Logic OR Gate" reverts to a LOW state only when ALL of its inputs are set to a logic level 0. Essentially, for a logic OR gate, any input at a HIGH state results in a HIGH, logic level 1 output.


Circuit


2-input Transistor OR Gate Circuit


A basic 2-input inclusive OR gate can be assembled using RTL (Resistor-Transistor Logic) with resistor-transistor switches interconnected, as illustrated below, where the inputs are directly linked to the transistor bases. For an output at Q, either transistor must be saturated, signifying an "ON" state.


2-input Transistor OR Gate circuit diagram.png


Digital circuits create Logic OR Gates, providing the desired logical function. These gates are symbolically represented, with their shape reflecting the logical operation of OR.


Truth Table


The Truth table of a 2-input OR Gate


BAQ
000
011
101
111


The Truth table of a 3-input OR Gate


CBAQ
0000
0011
0101
0111
1
001
1011
1101
1111


Logic Symbol and Boolean Expression


The 2-input Logic OR Gate

The 2-input Logic OR Gate symbol.png

Boolean Expression Q = A+B


The 3-input Logic OR Gate


The 3-input Logic OR Gate symbol.png

Boolean Expression Q = A+B+C


Applications


Primary Applications of OR Logic Gate:


  • Employed in circuits where multiple power sources are utilized to execute similar actions.

  • Implemented alarm systems and intrusion detection equipment.

  • Used in industrial plants for specific protective measures.


OR Gate IC


The prevalent integrated circuits (ICs) featuring OR gates include:


In TTL Logic:


74LS32 Quad 2-input


In CMOS Logic:



Universal Gates: NAND and NOR Gate


It is possible to execute any Boolean expression using exclusively either NAND gates or NOR gates. Consequently, NAND and NOR gates are considered universal gates. And tt's possible to implement a NOR gate using a NAND gate.


NAND and NOR gates serve as complements to the AND and OR gates. Their truth tables mirror the output states of the original gates but in reverse order.

The circuit symbols remain the same, with a small circle added to the output to signify the inversion of the logic level.


Boolean symbols change by placing a bar over the original expression: 


Universal Gates boolean symbols.png


Introducing a negated input to an AND gate enables the creation of inhibit/enable functionality.


Conclusion


In wrapping up our deep dive into logic gates, it becomes evident that these fundamental components are the bedrock of modern technology. Each plays a unique role, from NAND to AND, NOR to OR gates, contributing to the seamless functioning of electronic devices and systems.


Read More


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FAQ

  • What is the use of basic logic gates?
  • Basic logic gates carry out fundamental logical operations and are essential building blocks in integrated circuits.

  • What are the types of basic logic gates?
  • AND gate, OR gate, XOR gate, NAND gate, NOR gate, XNOR gate, and NOT gate constitute the seven fundamental types of logic gates.

  • What is the difference between the OR and NOR gates?
  • The NOR gate symbolizes the inverse of the OR operation, abbreviated as NOT OR. Its visual representation includes the OR symbol with a bubble at the output, indicating the execution of a complement operation on the OR gate's output.

  • What is the difference between NOR and NAND latch?
  • The NOR latch closely resembles the NAND latch, with the only distinction being the reversal of the Q and Q' outputs.

  • Why are NAND and NOR gates so popular?
  • Because NAND and NOR gates are cost-effective and simpler to manufacture, they are foundational in all IC digital logic families.

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