In the given Boolaen expression,
Y = A.B + B.Ā
if A=1, B=0 then Y will be
Answers
Answer:
boolean algebric laws
Explanation:
Annulment Law – A term AND‘ed with a “0” equals 0 or OR‘ed with a “1” will equal 1
A . 0 = 0 A variable AND’ed with 0 is always equal to 0
A + 1 = 1 A variable OR’ed with 1 is always equal to 1
Identity Law – A term OR‘ed with a “0” or AND‘ed with a “1” will always equal that term
A + 0 = A A variable OR’ed with 0 is always equal to the variable
A . 1 = A A variable AND’ed with 1 is always equal to the variable
Idempotent Law – An input that is AND‘ed or OR´ed with itself is equal to that input
A + A = A A variable OR’ed with itself is always equal to the variable
A . A = A A variable AND’ed with itself is always equal to the variable
Complement Law – A term AND‘ed with its complement equals “0” and a term OR´ed with its complement equals “1”
A . A = 0 A variable AND’ed with its complement is always equal to 0
A + A = 1 A variable OR’ed with its complement is always equal to 1
Commutative Law – The order of application of two separate terms is not important
A . B = B . A The order in which two variables are AND’ed makes no difference
A + B = B + A The order in which two variables are OR’ed makes no difference
Double Negation Law – A term that is inverted twice is equal to the original term
A = A A double complement of a variable is always equal to the variable
de Morgan’s Theorem – There are two “de Morgan’s” rules or theorems,
(1) Two separate terms NOR‘ed together is the same as the two terms inverted (Complement) and AND‘ed for example: A+B = A . B
(2) Two separate terms NAND‘ed together is the same as the two terms inverted (Complement) and OR‘ed for example: A.B = A + B
Other algebraic Laws of Boolean not detailed above include:
Boolean Postulates – While not Boolean Laws in their own right, these are a set of Mathematical Laws which can be used in the simplification of Boolean Expressions.
0 . 0 = 0 A 0 AND’ed with itself is always equal to 0
1 . 1 = 1 A 1 AND’ed with itself is always equal to 1
1 . 0 = 0 A 1 AND’ed with a 0 is equal to 0
0 + 0 = 0 A 0 OR’ed with itself is always equal to 0
1 + 1 = 1 A 1 OR’ed with itself is always equal to 1
1 + 0 = 1 A 1 OR’ed with a 0 is equal to 1
1 = 0 The Inverse (Complement) of a 1 is always equal to 0
0 = 1 The Inverse (Complement) of a 0 is always equal to 1
Distributive Law – This law permits the multiplying or factoring out of an expression.
A(B + C) = A.B + A.C (OR Distributive Law)
A + (B.C) = (A + B).(A + C) (AND Distributive Law)
Absorptive Law – This law enables a reduction in a complicated expression to a simpler one by absorbing like terms.
A + (A.B) = (A.1) + (A.B) = A(1 + B) = A (OR Absorption Law)
A(A + B) = (A + 0).(A + B) = A + (0.B) = A (AND Absorption Law)
Associative Law – This law allows the removal of brackets from an expression and regrouping of the variables.
A + (B + C) = (A + B) + C = A + B + C (OR Associate Law)
A(B.C) = (A.B)C = A . B . C (AND Associate Law)