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Digital Design—Combinational Logic
Published in Bogdan M. Wilamowski, J. David Irwin, Fundamentals of Industrial Electronics, 2018
Buren Earl Wells, Sin Ming Loo
It can be shown that any combinational function can be implemented using a combination of the basic AND, OR, and NOT operators. The corresponding set of gates is easily implemented in digital hardware in a manner that is dependent upon the underlying device technology. In Boolean algebra, a truth table can be used to show the values of the output for all possible values of the set of inputs. An example of the truth tables for all three of these main types of gates is shown in Figure 20.2. An AND gate is characterized by the fact that all inputs must be at a logic 1 before the output is a 1. An OR gate is characterized by the fact that if any of the inputs are at a logic 1, then the output is also at a logic 1, and a NOT gate simply inverts (switches) the value of its logic input. The functionality of applying the logic operations on the set of inputs to produce an output can also be expressed using Boolean algebra notation. In this notation, the input and outputs of a logical network are represented as variables or constants in much the same way as conventional algebraic statements. The operations performed by these three gates are expressed using standard algebraic symbols, where the AND operation represents Boolean multiplication, and the OR operation represents Boolean addition. By definition, the NOT operation is a unary operator. It is expressed by putting a line over the variable of interest.
C Programming
Published in Paul W. Ross, The Handbook of Software for Engineers and Scientists, 2018
Logic operators are logical and &&, logical or ||, and logical not!. These operators can be combined to form more complicated logical conditions. Such logical expressions are most often used to form conditions in control structures. The next section will provide several examples of these. The semantics of logical and (&&) are that the result is false (0) if either or both of the operands have a false value; if both operands are true, i.e., nonzero, then the logical and gives true. The logical or operator (||) is a binary one whose value is true if either or both of its operands are true, and is false when both are false. Logical not (!) is a unary operator that converts false to true or true to false.
Fragments of quasi-Nelson: residuation
Published in Journal of Applied Non-Classical Logics, 2023
Proposition 3.5 suggests that we can factor each quasi-Nelson monoid by the relation , obtaining a partial quotient algebra which is easily verified to be a bounded semilattice. The latter can be further endowed with a binary operation and a unary operation given by , the former acting as an implication and the latter as a nucleus. These properties, which we shall study abstractly in the next subsection, are consequences of the following lemma; for a proof we refer the reader to the Appendix, where we have also collected the lengthier proofs of several subsequent results.
On Soft Lattice Topological Spaces
Published in Fuzzy Information and Engineering, 2021
Let L be a complete lattice and its universal bounds denoted by ⊥ and ⊤. Assume that L is consistent i.e. ⊥ is distinct from ⊤. Thus for every Also and . The two point lattice is denoted by 2. A unary operation is quasi complementation. It is an involution (i.e. for all ) that inverts the ordering. (i.e. ). De Morgan's laws also hold in . (i.e. and for every ). Moreover, and . Based on these facts, in this paper we use a completely distributive lattice as a complete lattice equipped with an order reserving involution [10].
Epistemic space of degradation processes
Published in Journal of Applied Non-Classical Logics, 2021
The transformation of FDSs is defined as the unary operation such that , , where: .. is the quotient set of by ≡ (equivalence). is a mass assignment on satisfying .