Introduction to logic gate
- 1. Logic Gate Prof. Neeraj Bhargava Kapil Chauhan Department of Computer Science School of Engineering & Systems Sciences MDS University, Ajmer
- 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. AND operator It performs logical multiplication and denoted by (.) dot. X Y X.Y 0 0 0 0 1 0 1 0 0 1 1 1
- 4. OR operator It performs logical addition and denoted by (+) plus. X Y X+Y 0 0 0 0 1 1 1 0 1 1 1 1
- 5. NOT operator It performs logical negation and denoted by (-) bar. It operates on single variable. X X’ (means complement of x) 0 1 1 0
- 6. Truth Table 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.
- 7. Truth Table The truth table for XY + Z is as follows: Dec X Y Z XY XY+Z 0 0 0 0 0 0 1 0 0 1 0 1 2 0 1 0 0 0 3 0 1 1 0 1 4 1 0 0 0 0 5 1 0 1 0 1 6 1 1 0 1 1 7 1 1 1 1 1
- 8. Basic Concept If the output of Boolean expression is always True or 1 is called Tautology. If the output of Boolean expression is always False or 0 is called Fallacy. P P’ output (PVP’) output (PΛP’) 0 1 1 0 1 0 1 0
- 9. Application of Boolean algebra 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)
- 10. Exercise 1. Evaluate the following Boolean expression using Truth Table. (a) X’Y’+X’Y (b) X’YZ’+XY’ (c) XY’(Z+YZ’)+Z’ 2. Verify that (X+Y)’=X’Y’