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Digital Electronics Lecture 2 Logic Gates

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Lecture 2 outline Announcement: http://www.uobkupartnership.talktalk.net http://www.uobkupartnership.talktalk.net Review of last Lecture Logic Gates AND, OR, NOT, EX-OR, NAND, NOR Truth Tables Boolean equations

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Introduction to electronics Digital Electronics use many exciting applications Introduction to digital electronics Number systems: Decimal, binary and hex Converting from one number system into another Review of Last Lecture

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The AND gate The logical function of this gate may be expressed in words as follows: Y = A.B The Output, Y, of this gate is True only if all inputs to the gate are TRUE

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IC, AND gate

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The OR gate The logical function of this gate may be expressed in words as follows: Y = A+B+C The Output, Y, of this gate is True if any of the inputs to the gate are TRUE

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Overview of Electronics The logical function of this gate may be expressed in words as follows: B=A _ The Output, A, of this gate is True the input signal B is False

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NAND, NOR

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EX-OR gate The logical function of this gate may be expressed in words as follows: Y = A. B _ + A _.B

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INTEGRATED CIRCUIT (IC) LOGIC GATES 7408 AND gate 7432 OR gate 7404 NOT gate or Inverter 7400 NAND gate 7402 NOR gate 7486 XOR gate

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Turning equations into circuits It is always possible to produce a logic circuit which corresponds to a particular boolean expression, although it may contain many gates if the expression is a large, complicated one

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Circuit diagram

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BOOLEAN ALGEBRA The mathematical system of binary logic is called Boolean algebra or switching algebra. Boolean Theorems A- Single variable Theorems 1- A. 0 = 0 2- A. 1 = A 3- A. A = A 4- A. A _ = 0 5- A + 0 = A 6- A + 1 = 1 7- A + A = A 8- A + A _ =1

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BOOLEAN ALGEBRA (cont.) B- Multi Variable Theorems 9- A + B = B + A Commutative Laws 10- A. B = B. A 11- A + (B + C) = (A + B) +C Associative Laws 12- A. (B. C) = (A. B).C 13- A. (B + C) = A. B + A. C Theorems 9 to 13 are similar to ordinary algebra. 14- A + AB = A A.(1 + B) = A.1 = A 15- A + A _ B = A + B Equations 14 and 15 can be proved by truth table

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Main Points Logic gates AND, OR, NOT, Ex-OR, NAND, NOR Truth Tables Boolean Algebra

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The End Thank you for your attention.

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Chap. 3 Logic Gates and Boolean Algebra

Chap. 3 Logic Gates and Boolean Algebra

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