Boolean algebra is algebra associated with binary variables and logic operations. The variables are shown with letters of the alphabet, and three basic operations with AND, OR and NOT (complement). Boolean function consists of binary variables that indicate the function, an equal sign, and an algebraic expression formed by using binary variables, constants 0 and 1, the symbols of logic operations, and parentheses.
A Boolean function can be expressed in the truth table. A truth table for a Boolean function is a list of all combinations of binary digits 0 and 1 are assigned to the binary variables and a list that shows the value of the function for each binary combination. Boolean algebra has two distinct functions that are interconnected. In a broad sense, boolean algebra means a kind of symbols invented by George Boole to manipulate the values of truth algebraic logic.
In this case the boolean algebra suitable for application in the computer. On the other hand, boolean algebra is also an algebraic structure whose operations meet certain rules.
Dalil BOOLEAN;
1. X = 0 OR X = 1
2. 0. 0 = 0
3. 1 + 1 = 1
4. 0 + 0 = 0
5. 1. 1 = 1
6. 1. 0 = 0. 1 = 0
7. 1 + 0 = 0 + 1 = 0
THEOREM BOOLEAN
1. HK. commutative
A + B = B + A
A. B = B. A
2. HK. assosiative
(A + B) + C = A + (B + C)
(AB). C = A. (BC)
3. HK. Distributive
A. (B + C) = AB + AC
A + (BC) = (A + B). (A + C)
4. HK. negation
(A “) = A”
(A “)” = A
5. HK. ABRSORPSI
A + AB = A
A. (A + B) = A
6. HK. IDENTITY
A + A = A
A. A = A
7. DE MORGAN “S
(A + B) ‘= A “. B “
(A, B) ‘= A “+ B”
EXAMPLE:
1. A + A. B “+ A”. B = A. (1 + B “) + A”. B
= A. 1 + A “. B
= A + A “. B
= A + B
2. The series follows L
X = (AB) “. B = (A “+ B”). B
= A “.B
Or
