Tugas 4 Materi Rangkuman Aljabar Boolean
BOOLEAN ALGEBRA LAWS AND RULES
The law of commutative addition,
A + B = B + A
ORing order doesn't matter
Substitution of Multiplication Law
Substitution of Multiplication Law
AB = BA
the ANDing order doesn't matter.
The law of associative addition
The law of associative addition,
A + (B + C) = (A + B) + C
The ORed variable grouping does not matter
Associative law of multiplication
Associative law of multiplication
A (BC) = (AB) C
The ANDed variable grouping is not a problem
Distributive Law
A (B + C) = AB + AC
(A + B) (C + D) = AC + AD + BC + BD)
Boolean rules
1) A + 0 = A
Ÿ In math, if you add 0, you don't change anything
Ÿ In Boolean Algebra ORing with 0 doesn't change anything.
4) A • 1 = A
Ÿ RELING on anything by 1 will result in anything.
5) A + A = A
Ÿ ORing by itself will give the same result.
6) A + A = 1
Ÿ Either A or A must be 1 so A + A = 1.
7) A • A = A
Ÿ ANDing by itself will give the same result.
8) A • A = 0
Ÿ In digital logic 1 = 0 and 0 = 1, so AA = 0 because one of the inputs must be 0.
9) A = A
Ÿ If you don't do something twice you go back to the beginning.
10) A + AB = A
Proof:
A + AB = A (1 + B) DISTRIBUTIVE LAW
= A · 1 RULE 2: (1 + B) = 1
= RULE 4: A · 1 = A.
11) A + AB = A + B
Ÿ If A is 1 the output 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) FACTOR
= 1 (A + B) RULE 6
= A + B Rule 4
12) (A + B) (A + C) = A + BC
PROOF
(A + B) (A + C) = AA + AC + AB + BC LEGAL DISTRIBUTIVE
= A + AC + AB + BC RULE 7
= A (1 + C) + AB + BC FACTORING
= A.1 + AB + BC RULE 2
= A (1 + B) + BC FACTORING
= A.1 + SM RULE 2
= A + SM RULE 4
DITULIS : ANANDA BAGAS PRANATA
SUMBER : https://www.kabarmutiongkok.org/uhamka/last-lectur-2
https://onlinelearning.uhamka.ac.id
Komentar
Posting Komentar