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Logic Gates Shashidhara H S Dept. of ISE MSRIT

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Basic Logic Design and Boolean Algebra GATES = basic digital building blocks which correspond to and perform the basic logical functions. The three fundamental gates are: AND: Is a logical product. Its output = 1, only if both inputs are 1. Boolean Expression: A B “product” Logic Gate: Truth Table: Complex digital functions that make up a computer are built from these basic digital building blocks A B C ABC 000 010 100 111

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Basic Logic Design and Boolean Algebra · OR: Is a logical sum. Its output = 1 if either input = 1. Boolean Expression: A + B, “sum” Logic Gate: Truth Table: A B C ABC 000 011 101 111

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Basic Logic Design and Boolean Algebra NOT: Is a logical inversion since its output is opposite of its input. __ Boolean Expression: A or ~A, “not” Logic Gate: Truth Table A~A 0 1 1 0 AA _

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Laws of Boolean Algebra Identity law: A + 0 = A and A 1 = A Zero and One laws: A + 1 = 1 and A 0 = 0 Inverse Laws: A + A = 1and A A = 0 Commutative laws: A + B = B + A and A B = B A Associative laws: A + (B + C) = (A + B) + C and A (B C) = (A B) C Distributive laws: A (B + C) = (A B) + (A C) and A + (B C) = (A + B) (A + C) _____ __ __ De Morgan’s laws: (A + B) = (A) (B) and _____ __ __ (A B) = (A) + (B)

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More Logic Gates The basic digital building blocks for AND and OR can be combined with the NOT, inverter. The symbol used is a circle on the output. NAND: Is a NOT-AND. Its output = 1, only if both inputs are not 1. ____ Boolean Expression: A B Logic Gate: Truth Table: The NAND functions has traditionally been the universal gate in digital circuits. It is simple to implement in hardware and can be used to construct the other gates. A B C ABC 001 011 101 110

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More Logic Gates · NOR: Is a NOT-OR. Its output = 1 only if no input = 1. _____ Boolean Expression: A + B Logic Gate: Truth Table: A B C ABC 001 010 100 110

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More Logic Gates · XOR: Is an EXCLUSIVE-OR. Its output = 1 if the inputs are different and equal 0 if all are the same. Boolean Expression: A B Logic Gate: Truth Table: _ _ Logical equivalent: (AB) + (AB) = C ABC 000 011 101 110 A C B

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More Logic Gates · XNOR: Is an EXCLUSIVE-OR. Its output = 1 if the inputs are different and equal 0 if all are the same. Boolean Expression: A B Logic Gate: Truth Table: _ _ Logical equivalent: AB + AB = C ABC 001 010 100 111 A C B

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