“De Morgan’s laws”的概念、定义、翻译、参考文献-科学参考

De Morgan’s laws

Electronics and Electrical Engineering

Two mathematical laws of Boolean algebra that provide a means of expressing the complement (i.e. negation) of an expression in terms of the complements of individual elements of the expression:
$\begin{matrix} \bar{A + B + C + D + ...} & = & \bar{A} \cdot \bar{B} \cdot \bar{C} \cdot \bar{D} \cdot ... \\ \bar{A \cdot B \cdot C \cdot D \cdot ...} & = & \bar{A} + \bar{B} + \bar{C} + \bar{D} + ... \end{matrix}$
where + and · are the operators AND and OR and a horizontal bar denotes a complement. The laws provide a conversion between NAND and NOR gates (see logic circuit), and also enable a designer to move between positive and negative logic forms.

Philosophy

The equivalences (i) not-(A or B) if and only if not-A and not-B, and (ii) not-(A and B), if and only if not-A or not-B, are known as De Morgan’s laws, although De Morgan himself gave the equivalent statements in Boolean algebra. Each equivalence is a theorem of the propositional calculus.

单词	De Morgan’s laws
释义	De Morgan’s laws Electronics and Electrical Engineering Two mathematical laws of Boolean algebra that provide a means of expressing the complement (i.e. negation) of an expression in terms of the complements of individual elements of the expression: $\begin{matrix} \bar{A + B + C + D + ...} & = & \bar{A} \cdot \bar{B} \cdot \bar{C} \cdot \bar{D} \cdot ... \\ \bar{A \cdot B \cdot C \cdot D \cdot ...} & = & \bar{A} + \bar{B} + \bar{C} + \bar{D} + ... \end{matrix}$ where + and · are the operators AND and OR and a horizontal bar denotes a complement. The laws provide a conversion between NAND and NOR gates (see logic circuit), and also enable a designer to move between positive and negative logic forms. Philosophy The equivalences (i) not-(A or B) if and only if not-A and not-B, and (ii) not-(A and B), if and only if not-A or not-B, are known as De Morgan’s laws, although De Morgan himself gave the equivalent statements in Boolean algebra. Each equivalence is a theorem of the propositional calculus.
随便看	Hindenburg, Paul von (1847–1934) hindgut Hindu-Arabic number system Hinduism Hindu Mahasabha Hind’s Crimson Star Hind’s Variable Nebula hinge hinge line Hinode Hinotori Hinshelwood, Sir Cyril Norman Hinshelwood, Sir Cyril Norman (1897–1967) hinterland Hintikka, Jaakko (1929–2015) hip girdle Hipparchia Hipparchus Hipparchus of Nicaea (190–c.120) Hipparcos Hipparcos Catalogue Hippasus of Metapontum (6th) Hippias (c.485–415) Hippocamp hippocampus