5.boolean algebra
- 1. Boolean Algebra By Md. Fazle Rabbi 16CSE057
- 2. 4.2 Introduction It is described as an algebra of logic or an algebra of two values i.e True or False. The term logic means a statement having binary decisions i.e True/Yes or False/No
- 3. 4.3 It is used to perform the logical operations in digital computer. In digital computer True represent by ‘1’ (high volt) and False represent by ‘0’ (low volt) Logical operations are performed by logical operators. The fundamental logical operators are: 1. AND (conjunction) 2. OR (disjunction) 3. NOT (negation/complement) Application of Boolean algebra
- 4. 4.4 It performs logical multiplication and denoted by (.) dot. X Y X.Y 0 0 0 0 1 0 1 0 0 1 1 1 AND operator
- 5. 4.5 It performs logical addition and denoted by (+) plus. X Y X+Y 0 0 0 0 1 1 1 0 1 1 1 1 OR operator
- 6. 4.6 It performs logical negation and denoted by (-) bar. It operates on single variable. X X (means complement of x) 0 1 1 0 NOT operator
- 7. 4.7 Truth table is a table that contains all possible values of logical variables/statements in a Boolean expression. No. of possible combination = 2𝑛, where n=number of variables used in a Boolean expression. Truth Table
- 8. 4.8 Basic Theorem of Boolean Algebra T1 : Properties of 0 (a) 0 + A = A (b) 0 A = 0 T2 : Properties of 1 (a) 1 + A = 1 (b) 1 A = A T3 : Commutative Law (a) A + B = B + A (b) A B = B A T4 : Associate Law (a) (A + B) + C = A + (B + C) (b) (A B) C = A (B C) T5 : Distributive Law (a) A (B + C) = A B + A C (b) A + (B C) = (A + B) (A + C) (c) A+A’B = A+B T6 : Indempotence (Identity ) Law (a) A + A = A (b) A A = A
- 9. 4.9 Basic Theorem of Boolean Algebra T7 : Absorption (Redundance) Law (a) A + A B = A (b) A (A + B) = A T8 : Complementary Law (a) X+X’=1 (b) X.X’=0 T9 : Involution (a) x’’ = x T10 : De Morgan's Theorem (a) (X+Y)’=X’.Y’ (b) (X.Y)’=X’+Y’
- 10. 4.10 Logic Gate A gate is an digital circuit which operates on one or more signals and produce single output. Three type of gates are as under: 1. AND gate 2. OR gate 3. NOT gate
- 11. 4.11 Additional Boolean Operators • NAND, • NOR, • Exclusive-OR (Ex-OR) • Exclusive-NOR (Ex-NOR)