1. Lecture 4 Introduction to Boolean Algebra

2. Binary Operators In the following descriptions, we will let A and B be Boolean variables and define a set of binary operators on them. The term binary in this case does not refer to base-two arithmetic but rather to the fact that the operators act on two operands. unary operator NOT binary operators AND, OR, NAND, XOR

3. Logic Gates NOT AND OR XOR NAND NOR

4. F(A,B,C) = A + BC' Truth Tables A B C C' BC' A+BC' 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 1 1 1 0 1 1 0 0 0 1 0 0 1 0 1 1 0 1 0 0 1 1 1 0 1 1 1 1 1 1 0 0 1

5. A Boolean Function Implemented in a Digital Logic Circuit

6. Power Supply Input = 1 1 0 Voltmeter NOT gates AND gates OR gate(s) The Part of the Circuit Usually Not Shown

7. A One-Bit Adder Circuit

8. Venn Diagrams A AB AB AB AB AB A ~A + B A. B A+B A. B A=B A AB AB AB AB AB A ~A + B A. B A+B A. BA. B A=B

9. Three-Variable Venn Diagram F(A,B,C) = A + BC' 000 001 010 011 100 101 110 111 A B C A B C

10. De Morgan's Theorem A B A+B ~(A+B) ~A ~B (~A). (~B) ~(A+B)=(~A). (~B) 0 0 0 1 1 1 1 1 0 1 1 0 1 0 0 1 1 0 1 0 0 1 0 1 1 1 1 0 0 0 0 1 A B A+B ~(A+B) ~A ~B (~A). (~B) ~(A+B)=(~A). (~B) 0 0 0 1 1 1 1 1 0 1 1 0 1 0 0 1 1 0 1 0 0 1 0 1 1 1 1 0 0 0 0 1

11. Textbook Reading for Chapter 4