dlc logic gates ppt.pptx, boolean algebraic and logic gates
- 1. Department of Electrical and Electronics Engineering Course Name : Digital Logic Circuits Course Code : EE3302 Course Faculty : Dr M.Manjusha (Assistant Professor) (Dept. of EEE) (NAAC Accredited Institution) Run by Catholic Diocese of Marthandam Topic : BOOLEAN ALGEBRA AND LOGIC GATES
- 3. Developed by English mathematician George Boole in between 1815 - 1864. 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.
- 4. 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)
- 5. 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
- 7. 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
- 9. 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
- 11. • 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
- 12. PRACTICAL APPLICATIONS OF LOGIC GATES So while going out of the house you set the "Alarm Switch" and if the burglar enters he will set the "Person switch", and the the alarm will ring.
- 13. PRACTICAL APPLICATIONS OF LOGIC GATES The doorbell should ring when someone presses either the front door switch or the back door switch.
- 14. • Known as a “universal” gate because ANY digital circuit can be implemented with NAND gates alone NAND Gate
- 15. X X F = (X•X)’ = X’+X’ = X’ X Y Y F = ((X•Y)’)’ = (X’+Y’)’ = X’’•Y’’ = X•Y F = (X’•Y’)’ = X’’+Y’’ = X+Y X X F = X’ X Y Y F X•Y F = X+Y
- 16. NOR Gate NOR X Y Z X Y Z 0 0 1 0 1 0 1 0 0 1 1 0 Z = ~(X | Y) nor(Z,X,Y)
- 17. Exclusive-OR Gate X Y Z XOR X Y Z 0 0 0 0 1 1 1 0 1 1 1 0 Z = X ^ Y xor(Z,X,Y)
- 18. Exclusive-NOR Gate X Y Z XNOR X Y Z 0 0 1 0 1 0 1 0 0 1 1 1 Z = ~(X ^ Y) Z = X ~^ Y xnor(Z,X,Y)
- 19. 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
- 20. • 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
- 21. • T6 : Indempotence (Identity ) Law –(a) A + A = A (b) A A = A • T7 : Absorption (Redundance) Law –(a) A + A B = A (b) A (A + B) = A
- 22. • 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’
- 23. • Theorem 1 A . B = A + B De Morgan's Theorem
- 26. De Morgan's Theorem 2 • Theorem 1 A + B = A . B
- 29. Thank You