LAWS & RULES OF BOOLEAN ALGEBRA
Communitative law of addition
A + B = B+A
The order of or does not matter
Communitative law of multiplication
AB = BA
Associative law of addition
A + (B + C) = (A + B) + C
The grouping ORed variabels does not matter
Associative law of multiplication
A(BC) = (AB)C
The grouping ANDed variabels does not matter
DISTRIBUTIVE LAW
A(B+C) = AB + AC
(A+B)(C+B) = AC + AD + BC + BD
Boolean Rules
A + 0 =A
*in math if you adda 0 you have changed nothing
*in boolean algebra ORing tih 0 changes nothing
A + 1 =1
*ORing with 1 must give a 1 since if any input is 1 an OR gate will give a 1
A . 0 = 0
*in math if 0 is multiplied with anything you get 0. if you AND anything with 0 you get 0
A . 1 =1
*ANDing wnything with 1 will yield the anything
A + A = A
*ORing with itself will give the same result
A . A = A
*ANDing with itself will give the same result
A . A = 0
*in digital logic 1 = 0 and 0 =1 AA=0 since one of the inputs must be 0
A = A
*If you not something twice you are back to the beginning
A + AB = A
proof :
A + AB = A(1+B) DISTRIBUTIVE LAW
= A.1 RULE 2 : (1+B)=1
= A RULE 4: A.1=A
11. A + AB = A+B
if A is 1 the outputs is 1 ,If A is 0 the output is B
proof:
A + AB = (A + AB ) + AB RULE 10
= (AA + AB ) + AB RULE 7
= AA + AB + AA + AB RULE 8
= (A+ A)(A+B) FACTORING
= 1(A+B) RULE 6
=A+ B RULE 4
(A + B)(A + C ) = A + BC
sumber : https://onlinelearning.uhamka.ac.id/
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