Digital Electronics

Aug 6th, 2016
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Harvard University
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contains knowledgeable information on Boolean algebra, Laws and theorems of Boolean algebra(OR laws, AND laws, complementary laws, commutative laws, associative laws, distributive laws, absorptive laws, Inversion laws (De Morgan’s theorem), involution law and transposition theorem), Standard forms of Boolean expressions(the sum-of products (SOP) form and the product-of-sums (POS) form), Canonical SOP and POS, commonly used methods for the simplification of Boolean expressions.

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SPH 2433 Lecture 5 Sep-Dec 2015SPH 2433 Digital Electronics4.4. Boolean algebraBoolean algebra is the mathematics of logic.Among other differences, ordinary algebra differs from Boolean algebra in that: While ordinary algebra deals with many values including infinity, Boolean algebra deals with either of twovalues, that is, 0 and 1. The values assigned to a variable have a numerical significance in ordinary algebra, whereas in its Booleancounterpart they have a logical significance.There are three basic logical operators that are used in Boolean algebra: AND, OR, and NOT.These basic logical operators are based on a proposition i.e. a statement which can be characterized as either trueor false.For example, consider the statement:I will take an umbrella with me if it is raining or the weather forecast is bad This statement connects the proposition I will take an umbrella with me functionally to the two propositions itis raining and the weather forecast is bad.i.e. the umbrella proposition can be fully determined by the raining and weather propositions. Functionally, we can be consider the truth value of the umbrella proposition as the output of the truth values ofthe other two. This is represented by means of a simple block diagram shown in Figure 4-1.Figure 4-1: A simple proposition.The meaning of the OR connective is that the corresponding output is TRUE if either one of the input propositionsis T

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