Coding With Fun
Home Docker Django Node.js Articles Python pip guide FAQ Policy

How to complement all boolean expressions in boolean algebra?


Asked by Rosa Cooper on Nov 30, 2021 FAQ



Complement entire Boolean expression. Change all ORs to ANDs and all ANDs to ORs. Now, complement each of the variable and get final expression. will be first complemented, i.e. . Now, change all (+) to (.) and (.) to (+) i.e. Now, complement each of the variable, This is the final simplified form of Boolean expression,
Indeed,
Following are the important rules used in Boolean algebra. Variable used can have only two values. Binary 1 for HIGH and Binary 0 for LOW. The complement of a variable is represented by an overbar. Thus, complement of variable B is represented as .
Consequently, I used the fact that we can write any boolean variable A in the following way: A = A (B + B') = AB + AB' as (B + B') evaluates to 1 for any boolean variable B, so initial expression is not changed by AND-ing it together with such an expression. x'y + xy + xy'z + y' = y (x + x') + y' (xz + 1) = y + y' = 1.
Accordingly,
The variables used in Boolean Algebra only have one of two possible values, a logic “0” and a logic “1” but an expression can have an infinite number of variables all labelled individually to represent inputs to the expression, For example, variables A, B, C etc, giving us a logical expression of A + B = C, but each variable can ONLY be a 0 or a 1.
Similarly,
Boolean Algebra Laws and Rules. There are three laws of Boolean Algebra that are the same as ordinary algebra. The Commutative Law. addition A + B = B + A (In terms of the result, the order in which variables are ORed makes no difference.)