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> Other > The Ultimate Guide to Implementing NOR Gate from NAND Gate

The Ultimate Guide to Implementing NOR Gate from NAND Gate

업데이트 시간: 2023-11-24 14:34:48

Contents

NOR and NAND gates are universal logic gates, offering the capability to implement various logic gates and logical expressions. At the heart of modern electronics, these gates serve as the fundamental building blocks for constructing complex digital circuits. The NAND and NOR gates stand out for their versatility and significance. In this guide, we will explore how to skillfully transform a NAND gate into a NOR gate, demonstrating the adaptability and efficiency of these essential components in digital circuit design. By understanding the intricacies of the "NAND and NOR gate" relationship and specifically focusing on creating a "NOR gate from a NAND gate," we unlock new possibilities in electronics and digital logic design.


What is the NAND and NOR Gates?


In the following, we will discuss the NAND GATE and NOR GATE.


NAND gate


A NAND gate, also called a 'NOT-AND' or Negated Gate, is essentially a combination of a NOT gate followed by an AND gate. It holds the status of being one of the Universal Gates.


NOR Gate = OR Gate + NOT Gate


The output of this gate is 1 only when none of the inputs is 1. Alternatively, the output is high when all inputs are not high and at least one is low.

For two inputs, A and B, the Boolean expression for the NAND gate is Y = (A . B)'. The output is the opposite of the AND gate for all possible input combinations in the NAND gate. The NAND gate adheres to the commutative law, expressed as (AB)' = (BA)'. Here, A and B represent the inputs, and Y represents the output. The NAND logic gate can be implemented by multiplying all the inputs and complementing the result.


Symbol

symbol of NANDgate.png


Output Equation of NAND Gate


If A and B represent the input variables, and Y represents the output variable of the NOR gate, the output is determined by the expression:

Output Equation of NAND Gate.png


This is pronounced as "Y equals not A or not B."


Truth Table of Nand Gate


The chart illustrating the connection between inputs and the output of a logic gate is known as a truth table. Below is the truth table for the NAND gate:


InputOutput
ABY = (A + B)'
001
011
101
110


NOR gate


The NOR gate, denoted as the negated OR, produces a high output (1) when both inputs register a low state (0). Functioning as one of the Universal Gates, the NOR gate is occasionally called a "NOT-OR" gate, constructed by placing an OR gate followed by a NOT gate.


This gate's output assumes a high state (1) exclusively when all inputs reach a low state (0). Conversely, when all inputs are at a low level, the output becomes high. The Boolean representation for the NOR gate is expressed as Y=(A+B)’ when incorporating two inputs, A and B. Additionally recognized as the active LOW AND gate, the NOR gate's logic operation involves summing all inputs and subsequently complementing the result.


A and B denote the inputs in this context, while Y signifies the output. The NOR logic gate's functionality is achieved by summing all inputs and then complementing the summation result.


Symbol

sybmol of NORgate.jpg


Output Equation of NOR Gate


In the context where A and B serve as input variables, and Y represents the output variable of the NAND gate, the output can be expressed as follows:

Output Equation of NOR Gate.png


This expression is vocalized as "Y equals A dot B complement."


Truth Table of NOR Gate


The following is the truth table of the NAND gate:


InputOutput
ABY = (A + B)'
001
010
100
110


Difference between NAND Gate and NOR Gate


ParameterNAND GateNOR Gate
ExecutesThe NAND Gate performs negated logical multiplication.The NOR Gate performs negated logical addition.
Represent

The NAND Gate is symbolized by a (.)'.


Example: Z = (A.B)

The NOR Gate is symbolized by a (+)'.


Example: Z = (A+B)'

True OutputA NAND Gate produces a true output when precisely one input is true.A NOR Gate produces a true output only when both inputs are false.
High outputThe NAND Gate produces a high output if only one of its inputs is high.The NOR Gate produces a high output only if all of its inputs are low.
CombinationThe NAND Gate is formed by combining a NOT GATE and an AND GATE.The NOR Gate is formed by combining a NOT GATE and an OR GATE.


Why are there NAND and NOR gates?


Why do we create NAND and NOR gates instead of stringing together AND, OR, and NOT whenever the need arises? Although we have yet to delve into the construction of logic gates, there are compelling reasons to define NAND and NOR.


  • Electronic circuits inherently exhibit inversion: Whether employing MOSFETs or BJT transistors, the simplest circuit for implementing AND or OR functions naturally yields an inverted output signal "at no cost." If a non-inverting gate is desired, an additional inverter must be introduced to counteract the "free" inversion.

  • Simplicity correlates with compactness: The objective is to utilize the fewest transistors and gates possible. A NAND gate consistently occupies less space than an AND gate in gate arrays, semi-custom ASICs, or custom integrated circuits. Similarly, a NOR gate is invariably smaller than its OR gate counterpart.

  • Simplicity translates to speed: The naturally inverting NAND gate consistently outpaces an AND + NOT combination in speed.

  • Simplicity contributes to power efficiency: Simple gates entail fewer nodes changing each logic transition. A reduction in moving nodes results in less charge oscillation, necessitating less charge from the power supply. This translates to a prolonged battery life for your digital device—imagine your mobile phone retaining an account for a month instead of just a day.


What does the NAND gate use for?


The NAND gate is considered a universal gate as it can implement the functions of AND, OR, and NOT. NAND gates play a crucial role in identifying a low state in a single input of a digital system. For instance, a basic security system exclusively employing NAND gates can monitor the condition of sensors linked to windows and/or doors. When a window/door is shut, the sensor transmits a logical "1" signal to the security system. The alarm output remains at "0" as long as all windows and doors are closed. However, if any window or door opens, the security system output transitions to "1," triggering an alarm or initiating another specified action.


The prevalence of the NAND gate stems from its simplicity in implementation using transistor technology. For instance, a two-input NAND gate requires only four transistors in a CMOS configuration. All other logical operators can be constructed using exclusively NAND gates arranged in different configurations. This elementary circuit was the sole implementation in the early stages of microprocessor development.


Numerous real-life applications showcase the versatility of NAND gates, including:


  • Integration into alarm circuits based on light detection radiation.

  • Utilization of freezer warning buzzer devices.

  • Inclusion in automatic temperature regulation circuits.

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

  • Deployment in burglar alarm systems.


How to Implement NOR Gate from NAND Gate


Step-by-Step Guide Procedure


  1. Position the 74LS02 Quad 2-input NOR Gates IC onto the IC Trainer Kit.

  2. Establish connections for VCC and ground to the designated pins on the IC Trainer Kit.

  3. Assemble the circuit following the configuration outlined in the provided circuit diagram.

  4. Link the inputs to the set input switches available on the IC Trainer Kit.

  5. Connect the outputs to the switches associated with Output LEDs.

  6. Apply diverse input combinations under the truth table, observing the status of LEDs.

  7. Record the corresponding output readings for the varied input combinations.

  8. Power down the Trainer Kit, detach all wire connections and remove the ICs from the IC-Base.


Theory


NAND Gate - This digital circuit, equipped with two or more inputs, generates an output representing the logical AND of all the inverted inputs.


Digital circuits employ Logic NAND Gates to achieve specific logical functions. These gates are symbolized by a shape resembling a typical AND gate, featuring a circle, often referred to as an "inversion bubble," at the output. This symbol corresponds to the NOT gate and signifies the logical operation inherent in the NAND gate.


Similar to the previously discussed AND function, the NAND function supports any number of individual inputs. Commercially available NAND Gate ICs come in standard 2, 3, or 4 input configurations. Should additional inputs be necessary, the standard NAND gates can be interconnected to accommodate more inputs.


Boolean Expression Y = (A.B)'


"When either A or B is NOT true, Y is true."

nand gate theory.png


The operation of a NAND gate mirrors that of an AND gate followed by an inverter. This correlation is visually depicted in the symbol used to represent the NAND gate.


NOR GATE - A digital circuit featuring two or more inputs that yields an output, representing the inversion of the logical OR operation applied to all these inputs.


Digital circuits employ Logic NOR Gates to achieve specific logical functions. Symbolized by a shape resembling a standard OR gate, it incorporates a circle, often referred to as an "inversion bubble," at the output. This symbol signifies the NOT gate operation inherent in the NOR gate.


Similar to the OR function, the NOR function accommodates any number of individual inputs. Commercial NOR Gate ICs are readily available in standard 2, 3, or 4 input configurations. Should additional inputs be necessary, standard NOR gates can be interconnected to expand the input capacity.


Boolean Expression Y = (A+B)'


"When neither A nor B is true, Y is true."

nor gate theory.png


The operation of a NOR gate mirrors that of an OR gate followed by an inverter. This correspondence is visually represented in the symbol used to denote the NOR gate.


Block Diagram

nor gate from nand gate Block Diagram.png


Precautions


  1. Adhere to the IC pin diagram when establishing connections.

  2. Ensure secure connections on the trainer kit.

  3. Apply Vcc and ground meticulously to the designated pin.




Conclusion


In conclusion, implementing a NOR gate from a NAND gate opens up new possibilities in digital circuit design. The flexibility and efficiency of NOR gates make them a valuable asset in various applications. Whether you're a student, hobbyist, or professional, mastering the art of NOR gate implementation is a worthwhile endeavor.


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FAQ

  • Why do we use NAND gates instead of NOR gates?
  • The NAND gate incorporates cascaded NMOS in the pull-down network and parallel PMOS in the pull-up network.

  • Why is NAND more preferable than NOR?
  • NAND demonstrates superior efficiency in write operations, erasures, and sequential reads.

  • What is the minimum number of NOR gates required to release the NAND gate?
  • 1 NOR gate and 4 NAND gates.

  • What are logic gates using NOR gate and NAND gate?
  • The NAND gate generates a logic 1 output only when all its inputs are logic 0. In contrast, the NOR gate produces a logic 1 output only when one or more of its inputs are logic 0.

  • What are the basic logic gates?
  • Seven basic logic gates exist: AND, OR, XOR, NOT, NAND, NOR, and XNOR.

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