Logic Gates Pdf Notes Download REPACK

A logic gate is a device that acts as a building block for digital circuits. They perform basic logical functions that are fundamental to digital circuits. Most electronic devices we use today will have some form of logic gates in them. For example, logic gates can be used in digital electronics such as smartphones and tablets or in memory devices.

In a circuit, logic gates work based on a combination of digital signals coming from its inputs. Most logic gates have two inputs and one output, and they are based on Boolean algebra. At any given moment, every terminal is in one of the two binary conditions: true or false. False represents 0, and true represents 1.

Logic Gates Pdf Notes Download

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Depending on the type of logic gate being used and the combination of inputs, the binary output will differ. A logic gate can be thought of like a light switch, where in one position the output is off (0), and in another, it is on (1). Logic gates are commonly used in integrated circuits (IC).

The AND gate is named so because, if 0 is false and 1 is true, the gate acts in the same way as the logical "and" operator. The following illustration and table show the circuit symbol and logic combinations for an AND gate. (In the symbol, the input terminals are on the left, and the output terminal is on the right.) The output is "true" when both inputs are "true." Otherwise, the output is "false." In other words, the output is 1 only when both inputs are 1.

The OR gate gets its name from behaving like the logical inclusive "or." The output is true if one or both of the inputs are true. If both inputs are false, then the output is false. In other words, for the output to be 1, at least one input must be 1.

The XOR (exclusive-OR) gate acts in the same way as the logical "either/or." The output is true if either, but not both, of the inputs are true. The output is false if both inputs are "false" or if both inputs are true. Similarly, the output is 1 if the inputs are different but 0 if the inputs are the same.

A logical inverter, sometimes called a NOT gate to differentiate it from other types of electronic inverter devices, has only one input. A NOT gate reverses the logic state. If the input is 1, then the output is 0. If the input is 0, then the output is 1.

The NAND (Negated AND) gate operates as an AND gate followed by a NOT gate. It acts in the manner of the logical operation "and" followed by negation. The output is false if both inputs are true. Otherwise, the output is true. Another way to visualize it is that a NAND gate inverts the output of an AND gate. The NAND gate symbol is an AND gate with the circle of a NOT gate at the output.

Complex operations can be performed using combinations of these logic gates. In theory, there is no limit to the number of gates that can be arrayed together in a single device. But in practice, there is a limit to the number of gates that can be packed into a given physical space.

Arrays of logic gates are found in digital ICs. As IC technology advances, the required physical volume for each individual logic gate decreases, and digital devices become capable of performing more complicated operations at increasing speeds.

Quantum computers also have their own version of logic gates, called quantum logic gates, or qutrit quantum gates, which is a quantum circuit that operates using a small number of qutrits, which are qubits that have one added dimension. Similar to how logic gates are the building blocks of digital circuits, qutrit quantum gates are the building blocks of quantum circuits.

High or low binary conditions are represented by different voltage levels. The logic state of a terminal can, and generally does, change as the circuit processes data. In most logic gates, the low state is approximately zero volts (0 V), while the high state is approximately five volts positive (+5 V).

Logic gates can be made of resistors, transistors or diodes. These components are wired together in specific configurations to ensure they transform the inputs in expected ways. Resistors, for example, can commonly be used as a pull-up or pull-down resistor. Pull-up and pull-down resistors are used when there are any unused logic gate inputs to connect to a logic level 1 or 0. This prevents any false switching of the gate. Pull-up resistors are connected to Vcc (+5 V), and pull-down resistors are connected to ground (0 V).

Commonly used logic gates are transistor-transistor logic (TTL) and complementary metal-oxide-silicon (CMOS). TTL ICs use negative-positive-negative and positive-negative-positive bipolar junction transistors. CMOS ICs are constructed from metal-oxide-semiconductor or junction-gate field effect transistors. TTL ICs might commonly be labeled as the 7400 series of chips, while CMOS ICs may often be marked as a 4000 series of chips.

Logic gates are an important concept if you are studying electronics. These are important digital devices that are mainly based on the Boolean function. Logic gates are used to carry out logical operations on single or multiple binary inputs and give one binary output. In simple terms, logic gates are the electronic circuits in a digital system.

Logic gates have a lot of applications, but they are mainly based on their mode of operations or their truth table. Basic logic gates are often found in circuits such as safety thermostats, push-button locks, automatic watering systems, light-activated burglar alarms and many other electronic devices.

One of the primary benefits is that basic logic gates can be used in various combinations if the operations are advanced. Besides, there is no limit to the number of gates that can be used in a single device. However, it can be restricted due to the given physical space in the device. In digital integrated circuits (ICs), we will find an array of the logic gate area unit.

The logic gate, which gives a high output (i.e., 1) if either input A or input B but not both are high (i.e. 1), is called the exclusive OR gate or the XOR gate. It may be noted that if both the inputs of the XOR gate are high, then the output is low (i.e., 0).

Recent experimental breakthroughs have finally allowed to implement in-vitro reaction kinetics (the so called enzyme based logic) which code for two-inputs logic gates and mimic the stochastic AND (and NAND) as well as the stochastic OR (and NOR). This accomplishment, together with the already-known single-input gates (performing as YES and NOT), provides a logic base and paves the way to the development of powerful biotechnological devices. However, as biochemical systems are always affected by the presence of noise (e.g. thermal), standard logic is not the correct theoretical reference framework, rather we show that statistical mechanics can work for this scope: here we formulate a complete statistical mechanical description of the Monod-Wyman-Changeaux allosteric model for both single and double ligand systems, with the purpose of exploring their practical capabilities to express noisy logical operators and/or perform stochastic logical operations. Mixing statistical mechanics with logics and testing quantitatively the resulting findings on the available biochemical data, we successfully revise the concept of cooperativity (and anti-cooperativity) for allosteric systems, with particular emphasis on its computational capabilities, the related ranges and scaling of the involved parameters and its differences with classical cooperativity (and anti-cooperativity).

Such striking outcomes also arouse a great theoretical attention aimed to develop a self-contained framework able to highlight their potentialities and suggest possible developments. In particular, statistical mechanics has proved to be a proper candidate tool for unveiling biological complexity: in the past two decades statistical mechanics has been applied to investigate intra-cellular (e.g. metabolomics23,24, proteinomics25,26) as well as extra-cellular (e.g. neural networks3,27, immune networks28,29) systems. Also, statistical mechanics intrinsically offers a partially-random scaffold which is the ideal setting for a stochastic logic gate theory.

Another route to unveil the spontaneous information processing capabilities of biological matters is naturally constituted by information theory (see e.g. Refs. 30, 31 and references therein): remarkably, statistical mechanics and information theory (see the seminal works by Khinchin32,33 and by Jaynes34,35) and, in turn, information theory and logics (see the seminal works by Von Neumann36 and by Chaitin37) have been highlighted to be deeply connected. Therefore, it is not surprising that even in the quantitative modeling of biological phenomena these two routes are not conflicting but, rather, complementary.

In this work, we will use the former (statistical mechanics) to describe a huge variety of biochemical allosteric reactions and then, through the latter (mathematical logic), we will show how these reactions naturally encode stochastic versions of boolean gates and are thus capable of noisy information processing.

We will especially focus on allosteric reactions (as those of Koshland, Nemethy and Filmer (KNF)38 and Monod-Wyman-Changeaux (MWC)39) as they play a major role in enzymatic processes for which a great amount of experimental data is nowadays available. However, classical reaction kinetics (i.e. those coded by Hill, Adair, etc.40) can also perform logical calculations and they have been set in a statistical mechanical scaffold in Ref. 19: along the paper we will deepen the crucial differences between the two types of kinetics -allosteric cooperativity versus standard cooperativity- when framed within statistical mechanics.

Here we consider MWC-like kinetics and we reformulate it into a statistical mechanical framework. We start by introducing terminology and parameters for mono-receptor/mono-ligand systems (playing for single input gates as YES and NOT) and then we expand such a scenario in order to account for the kinetics of more complex systems (double-receptors/double-ligands, as those will play for two-input gates as AND, NAND, OR, NOR). 2351a5e196