1. Digital Electronics Lecture 2 Logic Gates

2. 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

3. 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

4. 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

5. IC, AND gate

6. 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

7. 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

8. NAND, NOR

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

10. 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

11. 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

12. Circuit diagram

13. 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

14. 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

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

16. The End Thank you for your attention.