Boolean logic algebra is the algebra of two values. These values are usually taken to be 0 and 1, as we shall do here, although F and T, false and true, etc. Boolean logic algebra are also a common uses of Boolean logic calculator. More generally Boolean algebra is algebra of values from any Boolean algebra as a model of the laws of Boolean algebra. In Boolean logic calculator first enter the expression then then enter the values of x and y. now press the calculate button then the answer will be produced.
Basic Operations Involved in Boolean Logic Calculator:
in Boolean logic calculator the operations mentioned below are involved automatically ,
After values, the next ingredient of any algebraic system has its operations. Whereas elementary algebra 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 multiplication is represented by a AND, an addition is represented by OR, and the NOT is represented with an over bar.
Conjunction was the closest of these three to its numerical counterpart, in fact on 0 and 1 it is multiplication. As the logical operation conjunction of two propositions is true when both propositions are true, and otherwise is false.
Disjunction works almost similar to addition in the boolean logic calculator, with one exception: the disjunction of 1 and 1 is neither 2 nor 0 but 1. Thus the disjunctions of two propositions are false when both propositions are false, and otherwise are true.
Logical negation does not work like numerical negation in the calculator. Instead it corresponds to incrementation: ¬x = x+1 mod 2. It shares the common numerical negation the property that applying it twice returns the original value: ¬¬x = x, just as −(−x) = x.
Some of the identities and operations involved in boolean logic is also in boolean logic calculator as,
(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
Problem Based on Boolean Logic Calculator:
Problem 1: Find the value for x.y = y.x
x y x.y y.x
0 0 0 0
0 1 0 0
1 0 0 0
1 1 1 1
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