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Lecture 1: An Introduction to Boolean Algebra. The operation of almost all modern digital computers is based on two-valued or binary systems. Binary systems were known in the ancient Chinese civilisation and by the classical Greek philosophers who created a well structured binary system, called propositional logic.
After studying this chapter you should. • be able to use AND, NOT, OR and NAND gates;. • be able to use combinatorial and switching circuits;. • understand equivalent circuits;. • understand the laws of Boolean algebra;. • be able to simplify Boolean expressions;. • understand Boolean functions;. • be able to minimise circuits
This chapter focuses on the construction of a family of simple chips called Boolean gates. Since Boolean gates are physical implementations of Boolean functions, we start with a brief treatment of Boolean algebra. We then show how Boolean gates implementing simple Boolean functions can be interconnected to deliver
input and output relationships. Logic Expressions for an OR Gate. The logical OR function of two variables is represented mathematically by a. + between the two variables, for example, A + B. Addition in Boolean algebra involves variables whose values are either binary 1 or binary 0. The basic rules for Boolean addition
1. Chapter 2. Boolean Algebra and Logic Gates. ?. The most common postulates used to formulate various algebraic structures are: 1. Closure. N={1,2,3,4}, for any a,b N we obtain a unique c N by the operation a+b=c. Ex:2?3= ?1 and. 2,3 N, while (?1) N. 2. Associative law. A binary operator * on a set S is said to.
Design a logic circuit with three inputs A, B, C and one output F such that F="1" only when a majority of the inputs is equal to 1. A B C F. Sum of product form. 0 0 0 0. F = A.B.C + A.B.C + A.B.C + A.B.C. 0 0 1 0. 0 1 0 0. 0 1 1 1. 1 0 0 0. 1 0 1 1. 1 1 0 1. 1 1 1 1. Draw a logic circuit to generate F
Boolean Algebra (Binary Logic). Theorem. A + 0 = A. A + 1 = 1. A A A. A * 0 = 0. A * 1 = A. A*A A. A + A = A. A + A' = 1. A * A = A. A * A' = 0. A + B = B + A. (A + B) + C = A + (B + C). AB + AC = A(B + C). A * B = B * A. (A * B) * C = A * (B * C). (A + B)*(A + C) = A + BC. AB + AC = A(B + C). (A + B) (A + C) = A + BC
Boolean Algebra (Binary Logic). {0, 1}. 0: Low. 0.0 Volt. 1: High. 5.0 Volt. Page 2. Boolean Algebra (Binary Logic). {0, 1}. 0: Low. 0.0 Volt. False. OFF. 1: High. 5.0 Volt. True. ON. Page 3. Boolean Algebra (Binary Logic). Operation. + : OR. Page 4. Boolean Algebra (Binary Logic). Operation. + : OR. 0+0=0 0+1=1 1+0=1 1+1=1
31 Aug 2006 Logic Gates (Introduction). The package Truth Tables and Boolean Algebra set out the basic principles of logic. Any Boolean algebra operation can be associated with an electronic circuit in which the inputs and outputs represent the statements of Boolean algebra. Although these circuits may be complex
Digital Electronics, 2003. Ovidiu Ghita. Page 1. Binary Logic and Boolean algebra. Boolean algebra: Devised for dealing mathematically with philosophical propositions which have ONLY TWO possible values: TRUE or FALSE, Light ON or OFF. SW1 Open >> Lamp is OFF. SW1 Closed >> Lamp is ON. Two states: SW1.
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