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Boolean Algebra
Published in Rowan Garnier, John Taylor, Discrete Mathematics, 2020
In this section we deal with ‘logic gates'. These are electronic devices which may be viewed as the basic functional components of a digital computer. A logic gate is an electronic component, incorporated within a circuit, which operates on one or more inputs to produce one output. Each input and each output can take one of two values (normally low and high voltage) which are denoted by 0 and 1. Because of the ‘two-value' nature of the input and output variables, a logic gate is an example of a binary device. It also falls in the category of combinational devices because the output value depends only on the input values. (This is in contrast to a sequential device where the output value is also determined by such factors as the time or the past history of the circuit.)
Functional Logics
Published in Michael Olorunfunmi Kolawole, Electronics, 2020
Many tasks in modern computer, communications, and control systems are performed by logic circuits. Logic circuits are made of gates. A logic gate is a physical device that implements a Boolean function that performs a logic operation on one or more logical inputs (or terminals) and produces a single logical output. This chapter examines the basic principles of logic gates: the types—from primitive to composite gates—and how they are arranged to perform basic and complex functions.
Introduction to Mechatronic Systems
Published in Bogdan M. Wilamowski, J. David Irwin, Control and Mechatronics, 2018
The arithmetic logic circuit is composed of a group logic gate that performs a Boolean logical operation on a set of meaningful logic inputs and produces a set of corresponding logic outputs. Logic gates are primarily implemented electronically using diodes or transistors, and a logic level is represented by a voltage or current, which depends on the type of electronic logic in use. A truth table is a table that describes the operational rules of a logic gate and lists the value of the output for every possible combination of the inputs. In order to obtain an efficient implementation, a minimization procedure, some optimizing approach, e.g., Karnaugh maps, the Quine–McCluskey algorithm, or a heuristic algorithm, is used to reduce the circuit complexity.
New theorems for inverting the functions of logic gates in digital circuits
Published in Journal of Control and Decision, 2022
Fundamentally, digital logic gates comprise the AND gate; NAND gate; OR gate, NOR gate, Inverter, Buffer, Exclusive OR (XOR) gate and Exclusive NOR (XNOR) gate (John, 2002; Nehinbe, 2022; Onan, 2022; Opara & Kania, 2010; Takbiri et al., 2022). The premise of this paper is that the existing gates have given rise to the combinational circuits, evolution of new theorems and sequential circuits that require new interpretations. Therefore, this paper intends to further extend the classical work of Nehinbe (2022) and then introduces the concept of diagonal search to explain the relationships between the elements of the digital logic circuits and the Truth Tables. The contributions of this paper are as follows: The paper determines the behaviour of digital logic networks by considering possible variations of the AND, OR and NOT gates while designing digital circuits. The paper proposes new theorems for inverting the functions of six different logic gates in logic circuits and proofs them to enhance the analysis of digital logic networks. The paper affirms the use of perfect induction of diagonal, horizontal and the vertical elements of the Truth Tables in order to further elucidate digital logic operations and minimisation of undesirable noise that may occur due to the embedded elements of logic gates in logic tables.
Multiple-Controlled Toffoli and Multiple-Controlled Fredkin Reversible Logic Gates-Based Reversible Synchronous Counter Design
Published in IETE Journal of Research, 2023
S. K. Binu Siva Singh, K. V. Karthikeyan
Quantum gates are the building blocks of quantum circuits, and they manipulate the state of qubits. In classical computing, logic gates such as AND, OR, and NOT gates are used to manipulate the state of bits. In quantum computing, there are a few universal gates that can be utilized to construct quantum circuits. One of these is the Toffoli gate, a three-qubit gate that functions similarly to a conventional AND gate. Another three-qubit gate is the Fredkin gate, also known as the controlled-SWAP gate, which swaps the second and third qubits if the first qubit is in the state.
Design of testable reversible latches by using a novel efficient implementation of Fredkin gate
Published in International Journal of Electronics, 2020
Zahra Mohammadi, Keivan Navi, Reza Sabbaghi-Nadooshan
As the basic elements of any logic circuit, logic gates are used to realise Boolean functions. By using reversible logic gates, reversible circuits can be constructed that perform complex logical and arithmetic operations. Some gates, such as the Feynman, Fredkin, and Toffoli gates, have been employed by many reversible logic circuits.