Boolean Logic Expression
Boolean logic Expression is an algebraic expression of two values. These values are generally taken as T and F, as we shall do here, although 0 and 1, false and true, etc. are also a common uses of Boolean logic gates. More generally Boolean logic Expression is an algebraic Expressions of values from any laws of Boolean logic operations.
Basic Boolean Logic Expression
The next component of an algebraic system has its own operations, such as basic Boolean logic expressions was based on numeric operations multiplication x • y, addition x + y, and negation −x,
Boolean logic algebra calculator is customarily based on logical counterparts to those operations, namely conjunction x • y (AND), disjunction x + y (OR), and complement or negation ¬x (NOT). In
electronics, the product is characterized by a AND, an addition is characterized by OR, and the NOT is characterized with an over bar.
Conjunction is the neighboring of these three to its numerical complement, in fact on 0 and 1 it is product. As the logical expression conjunction of two values is true when both values are true, and otherwise is false.
Disjunction functions nearly similar to addition in the Boolean logic expressions, with one exceptional case, i.e. the disjunction of 1 and 1 should be either 2 or 0 but it is 1. Thus the disjunctions of two values are false when both of the values are false, and otherwise are true.
Logical negation does not function like numerical negation in the expressions. Instead it matches to incrementation, ¬x = x + 1 mod 2. Logical negation expression shares the general numeric negation
property which applies twice to return the original value, i.e. ¬¬x = x, just as − (−x) = x.Identities in Boolean Logic Expression
(1a) x • y = y • x (1b) x + y = y + x (1c) 1 + x = 1
(2a) x • (y • z) = (x • y) • z (2b) x + (y + z) = (x + y) + z
(3a) x • (y + z) = (x • y) + (x • z) (3b) x + (y • z) = (x + y) • (x + z)
(4a) x • x = x (4b) x + x = x
(5a) x • (x + y) = x (5b) x + (x • y) = x
(6a) x • x1 = 0 (6b) x + x1 = 1
(7) (x1)1 = x
(8a) (x • y)1 = x1 + y1 (8b) (x + y)1 = x1 • y1