Ans-:BOOLEAN ALGEBRA -:
Boolean algebra or switching algebra is a system of mathematical logic to perform different mathematical operations in binary system. There is only three basis binary operations, AND, OR and NOT by which all simple as well as complex binary mathematical operations are to be done. There are many rules in Boolean algebra by which those mathematical operations are done. In Boolean algebra, the variables are represented by Capital Letter like A, B, C etc and the value of each variable can be either 1 or 0, nothing else. In Boolean algebra an expression given can also be converted into a logic diagram using different logic gates like AND gate, OR gate and NOT gate, NOR gates, NAND gates, XOR gates, XNOR gates etc.
Some basic logical Boolean operations
|
AND
OPERATION |
OR
OPERATION |
NOT
OPERATION |
|
0.0=0 |
0+0=0 |
(1)’=0 |
|
1.0=0 |
0+1=1 |
(0)’=1 |
|
0.1=0 |
1+0=1 |
|
|
1.1=1 |
1+1=1 |
|
Some basic laws and theorems for Boolean Algebra:
1] Idempotent Law : (i) A + A = A (ii) A . A = A
2] Commutative Law : (i) A+ B = B+ A (ii) A. B = B . A
3] Associative Law : (i) (A + B) + C = A + (B+ C) (ii) (A . B) . C = A . ( B . C)
4] Distributive Law : (i) A + (B . C) = (A + B) . (A+ C) (ii) A . (B+ C) = ( A . B)+ ( A . C)
5] Complement Law : (i) A + A’ = 1 (ii) A . A’ = 0
6] Double Complement Law : (A’)’ = A
7] Identity Law : (i) A + 0 = A (ii) A . 1 = A
8] Null ( Dominance ) Law : (i) A + 1 = 1 (ii) A . 0 = 0
9] Absorption Law : (i) A. (A + B) = A (ii) A + (A . B) = A (iii) A . (A’+B) = ( A . B )
(iv) A + A’. B = ( A + B )