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# Digital Electronics Lecture 2 Logic Gates. Lecture 2 outline Announcement:

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Digital Electronics Lecture 2 Logic Gates

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

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

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

IC, AND gate

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

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

NAND, NOR

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

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

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

Circuit diagram

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

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

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

The End Thank you for your attention.

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