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# Boolean Algebra

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1. Boolean Algebra D. W. ChathurikaPavithrani UvaWellassa University

2. The digital circuitry in digital computers and other digital systems is designed, and its behavior is analyzed, with the use of mathematical discipline known as Boolean Algebra.

3. Basic Logical Operations • AND • Represented by a dot or by the absence of an operator • OR • Represented by a Plus symbol • Not • Represented by a Bar over the variable

4. Logical AND Operation • 0 . 0 = 0 • 0 . 1 = 0 • 1 . 0 = 0 • 1 . 1 = 1

5. Logical OR Operation • 0 + 0 = 0 • 0 + 1 = 1 • 1 + 0 = 1 • 1 + 1 = 1

6. D = A + (B’ + C) D equals to 1 if A is 1 or if both B = 0 and C = 1

7. Logical XOR Operation • 0 . 0 = 0 • 0 . 1 = 1 • 1 . 0 = 1 • 1 . 1 = 0

8. Logical NAND Operation • 0 . 0 = 1 • 0 . 1 = 1 • 1 . 0 = 1 • 1 . 1 = 0

9. Logical NOR Operation • 0 . 0 = 1 • 0 . 1 = 0 • 1 . 0 = 0 • 1 . 1 = 0

10. Boolean Operators

11. A + B . C = A + (B.C) = A + BC

12. A NAND B = NOT(A AND B) = (AB)’ A NOR B = NOT (A OR B) = (A + B)’

13. Basic Postulates Commutative laws Distributive laws Identity elements Inverse elements

14. Other Identities Associative Laws DeMorgan’s Theorem

15. A NOR B = A’ AND B’ A NAND B = A’ OR B’