Logic gates with laws in digital electronics

1. LOGIC GATES WITH LAWS
BY NIKHIL ARORA
(WWW.INTERNETNOTES.IN)

2. Cumulative Law
• the order of OR operations and AND
operations conducted on the variables makes
no differences.
• (a) A + B = B + A
(b) A B = B A
• or

3. Cumulative Law

4. Associative Laws
• This law is for several variables, where the OR
operation of the variables result is same
though the grouping of the variables. This law
is quite same in case of AND operators.
• (A + B) + C = A + (B + C)
(A B) C = A (B C)

5. Distributive Laws
• This law is composed of two operators, AND
and OR
• (a) A (B + C) = A B + A C
(b) A + (B C) = (A + B) (A + C)

6. • Identity Law(a) A + A = A
(b) A A = A
• Redundance Law
• (a) A + A B = A
(b) A (A + B) = A

7. Negation Law

8. UNIVERSAL LAWS
• (a) 0 + A = A
(b) 1 A = A
(c) 1 + A = 1
(d) 0 A = 0

9. De Morgan’s Therem,

10. PROOF:

11. IMPORTANT
• EVERY LOGIC GATE FOLLOWS
COMMUTATIVE LAW

12. FOLLOWS ASSOCIATIVE LAWS
• AND
• OR
• EX-OR
• EX-NOR

13. DOESNOT FOLLOWS ASSOCIATIVE LAW
• NAND
• NOR
• BUT BOTH ARE UNIVERSAL GATE

14. FOLLOWS DISTRIBUTIVE LAW
• AND
• OR

15. DOESNOT FOLLOWS DISTRIBUTIVE
LAW
• EX-OR
• EX-NOR
• NAND
• NOR

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