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Combinational Logic Design Using Verilog HDL
Published in Joseph Cavanagh, Verilog HDL Design Examples, 2017
Theorem 6: Absorption law 2 This version of the absorption law is used to eliminate redundant variables from certain Boolean expressions. Absorption law 2 eliminates a variable or its complement and is a very useful law for minimizing Boolean expressions.x1 + (x1’ • x2) = x1 + x2x1 • (x1’ + x2) = x1 • x2
Minimization of Switching Functions
Published in Joseph Cavanagh, Digital Design and Verilog HDL Fundamentals, 2017
Theorem 6: Absorption law 2 This version of the absorption law is used to eliminate redundant variables from certain Boolean expressions. Absorption law 2 eliminates a variable or its complement and is a very useful law for minimizing Boolean expressions. x1 + (x1′ • x2 ) = x1 + x2x1 • (x1′ + x2) = x1 • x2
Logic Design Fundamentals
Published in Joseph Cavanagh, Computer Arithmetic and Verilog HDL Fundamentals, 2017
This version of the absorption law is used to eliminate redundant variables from certain Boolean expressions. Absorption law 2 eliminates a variable or its complement and is a very useful law for minimizing Boolean expressions.
A probabilistic framework for multi-hazard risk mitigation for electric power transmission systems subjected to seismic and hurricane hazards
Published in Structure and Infrastructure Engineering, 2018
where S0 is an arbitrary shortest path from the source to the demand node; is the complementary of S0; are components (nodes or edges) in S0; si and denote the survival and failure of component i, respectively; and Gi is the corresponding subgraph of G obtained by removing component i from the original graph. The first line of Equation (7) is derived based on the Boolean laws of set operation. is then expanded in the second line based on De Morgan’s law and absorption laws. In the third line, Boolean simplification is used to reduce G in the second line to the sub-graph Gi, which is obtained by deleting component si from the original network G. The result of the recursive decomposition is a set of disjoint path sets connecting the source node and the demand node. The accessibility of the demand node, which is the probability that there is at least one path from the source node to the demand node, is then calculated by summing the reliabilities of the disjoint path sets.