Laws & Ruleas of Boolean Algebra
* Commutative law of addition
A+B = B+A
the order of ORing does not matter
* Commutative law of Multiplication
AB = BA
the order of ANDing does not matter
* Associative law of addition
A + (B + C) = (A + B) + C
The grouping of ORed variables does not matter
* Assocoative law of multiplication
A(BC) = (AB)C
The grouping of ANDed variables does not matter
*Distributive Law
A(B + C) = AB + AC
2) A + 1 = 1
- ORing with 1 must give a 1 since if any input is 1 an OR gate will give a 1
3) A * 0 = 0
- In math if 0 is multiplied with anything you get 0. If you AND anything with 0 you get 0
4) A * 1 = A
- ANDing anything with 1 will yield the anything
5) A + A = A
- ORing with itself will give the same result
6) A + A = 1
- Either A or A must be 1 so A + A = 1
7) A * A = A
- ANDing with itself will give the same result
8) A * A = 0
- In digital Logic 1 = 0 and 0 = 1, so AA = 0 since one of the inputs must be 0
9) A = A
- If you not something twice you are back to the beginning
10) A + AB = A
Proof :
A + AB = A(1 + B) Distributive
= A * 1 Rule 2 : (1 + B) = 1
= A Rule 4 : A * 1 = A
11) A + AB = A + B
- If A is 1 the output is 1, if A is 0 output is B
12) (A + B)(A + C) = A + BC
Proof :
(A + B)(A + C) = AA + AC + AB+ BC Distributive Law
= 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 + BC Rule 2
= A + BC Rule 4
Sumber Artikel
Nama :Rafi Fadhlur Rahman
Nim : 2003015221
Kelas : 2F
https://onlinelearning.uhamka.ac.id
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