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A combinatorial circuit is a system containing basic boolean operations (AND, OR, NOT), some inputs, and a set of outputs. Since each output corresponds to an individual logic function, a combinatorial circuit often implements several different boolean functions. It is very important that you remember this fact – each output represents a different boolean function. A computer’s CPU is built up from various combinatorial circuits. For example, you can implement an addition circuit using boolean [...]

Since there are a finite number of boolean functions of n input variables, yet an infinite number of possible logic expressions you can construct with those n input values, clearly there are an infinite number of logic expressions that are equivalent (i.e., they produce the same result given the same inputs). To help eliminate possible confusion, logic designers generally specify a boolean function using a canonical, or standardized, form. For any given boolean function Buy [...]

Any boolean expression may be expressed in terms of either minterms or maxterms. To do this we must first define the concept of a literal. A literal is a single variable within a term which may or may not be complemented. For an expression with N variables, minterms and maxterms are defined as follows : A minterm is the product of N distinct literals where each literal occurs exactly once. A maxterm is the sum [...]

I’ve always confused “permutation” and “combination” — which one’s which? Here’s an easy way to remember: permutation sounds complicated, doesn’t it? And it is. With permutations, every little detail matters. Alice, Bob and Charlie is different from Charlie, Bob and Alice (insert your friends’ names here). Combinations on the other hand, are pretty easy going. The details don’t matter. Alice, Bob and Charlie is the same as Charlie, Bob and Alice. Permutations are for lists (order [...]

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Yesterday before submitting my assignment of the database, which was totally related to relational algebra queries, i got stuck in Division operator. I read the text book of Connolly “Introduction to Database System” But the formulas got me confused. Then eventually I’ve just got a copy of THE MANGA GUIDE TO DATABASES (ISBN 978-1-59327-190-9); it is one of a series of “Manga Guides” (the others are Calculus and Statistics).  Since I consider myself a long [...]