Ones and Zeros: Understanding Boolean Algebra, Digital Circuits, and the Logic of Sets
Wiley, 1998 - 281 pages
Ones and Zeros explains, in lay terms, Boolean algebra, the suprisingly simple system of mathematical logic used in digital computer circuitry. Ones and Zeros follows the development of this logic system from its origins in Victorian England to its rediscovery in this century as the foundation of all modern computing machinery. Readers will learn about the interesting history of the development of symbolic logic in particular, and the often misunderstood process of mathematical invention and scientific discovery, in general. Ones and Zeros also features practical exercises with answers, real-world examples of digital circuit design, and a reading list. Ones and Zeros will be of particular interest to software engineers who want to gain a comprehensive understanding of computer hardware. Outstanding features include: a history of mathematical logic, an explanation of the logic of digital circuits, and hands-on exercises and examples.
THE ALGEBRA OF SETS AND VENN
OTHER BOOLEAN FUNCTIONS
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abcd Absorption Law adder algebra of sets algebraic expression Associative Law axioms base 10 numbers binary number Blake canonical form Boole Boole's Boolean algebra Boolean expression Boolean function c₁ called circuit diagram combination of inputs Commutativity Law Complementation Law control input d₁ data input decoder DeMorgan's laws digit position digital circuits Distributive Law draw the Venn eight-bit equal equation equivalent example Exercise flip four input gate gray code implication function input bits interpretation intersection Karnaugh map mathematical system maxterm realization minions minterm minterm expression multiplexer NAND node number system output bit output column output line perfect induction possible combinations prime implicants principle of assertion represent seven-segment display shown in Figure shown in Table significant bit SOP expression Special Property subset teleport three sets three-input truth table two-input variables vector Venn diagram zero