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Boolean Algebra and Logic Gates
Published in Dale Patrick, Stephen Fardo, Vigyan ‘Vigs’ Chandra, Electronic Digital System Fundamentals, 2020
Dale Patrick, Stephen Fardo, Vigyan ‘Vigs’ Chandra
Boolean expressions are frequently used to describe how a logic circuit operates. We have used these expressions to construct circuits and to define operations. A logic circuit has several alternatives that must be taken into account when evaluating its operation. A graphic display of the operational steps and all its possible alternatives is sometimes needed to understand fully the operation of an expression. A display that shows these operations is called a truth table. A truth table is defined as a tabular listing of all the possible logic-level combinations produced by the input and output of a digital circuit. This means that a truth table is a specifications sheet that describes the exact behavior of a logic circuit. The circuit can have several inputs and one or more outputs.
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.
An introduction to digital logic
Published in Kirk Ross, Hunt Andy, Digital Sound Processing for Music and Multimedia, 2013
A truth table representation, as shown in Figure 6.1, is simply a listing of all possible combinations of inputs (usually represented in an ascending binary sequence), together with the output corresponding to each input combination. An input switch in the ‘ON’ state, or an active output state (light or boiler ON) is indicated with a ‘1’. The expression which would be used in the Boolean algebraic function equivalent to the operation of these systems is also shown for completeness. Figure 6.1(a) is the truth table for a three-input OR function, Figure 6.1(b) is that for a three-input AND function.
Harder, better, faster, stronger: digitalisation and employee well-being in the operations workforce
Published in Production Planning & Control, 2022
The analysis of sufficient causal conditions is carried out by creating a truth table. A truth table consists of three steps: (i) construction, (ii) reduction and (iii) analysis (Ragin 2008). Construction is performed by generating a truth table consisting of all the possible logical combinations of causal conditions that could create the presence of the outcome. Each row in the truth table represents one logical combination. The 2k possible combinations equal to 256 (28) rows in this context.
A novel integrated method of fsQCA and digital design for sustainability monitoring and assessment in building energy management systems: a case study
Published in Journal of Building Performance Simulation, 2023
Abdolvahhab Fetanat, Mohsen Tayebi, Gholamreza Shafipour, Mehran Moteraghi
Due to the results of fsQCA method, for drawing the circuit of study, three logical AND, OR and NOT gates are needed. In this regard, the truth tables and design of logic circuits are necessitated. Therefore, tables and graphic symbols of three AND, OR and NOT gates are shown in Table 4. These symbols provide a clear definition of the operation.
New theorems for inverting the functions of logic gates in digital circuits
Published in Journal of Control and Decision, 2022
We build Truth tables with different combinations of inputs to digital circuits. Thereafter, we search the elements for the occurrence of logic gates that are stated in the theorems within each Truth table. Each truth table is searched diagonally, horizontally, vertically downward and upward. The results obtained are shown below.