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Logic Gates

Logic Gates. Shashidhara H S Dept. of ISE MSRIT.

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Logic Gates

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  1. Logic Gates Shashidhara H S Dept. of ISE MSRIT

  2. Basic Logic Design and Boolean AlgebraGATES = 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

  3. 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

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

  5. 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)

  6. More Logic GatesThebasic 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

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

  8. 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 ÅBLogic Gate:Truth Table: __ Logical equivalent: (A•B) + (A•B) = C A C B

  9. 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 BLogic Gate:Truth Table: _ _ Logical equivalent: AB + AB = C A C B

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