Tugas 4. Rangkuman Materi Aljabar Boolean
Aturan – Aturan Aljabar Boolean
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 addition
A + (B + C) = (A + B) + C
The group of ORed variables does not matter
5
A (BC) = (AB) C
The group of ANDed variables does not matter
Distributive Law
A(B + C) = AB + AC
(A + B) (C + D) = AC + AD + BC + BD
BOOLEAN RULES :
1) A
+ 0 = A
In math if you add 0 you have changed
nothing
In
Boolean Algebra ORing with 0 changes nothing
2) A + 1 = 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)
= A * 1
= A
11) A
+ AB = A + B
Proof
A + AB
= (A + AB) + AB
= (AA + AB) + AB
= AA + AB + AA + AB
= (A + A) (A + B)
= 1* (A + B)
= A + B
12) (A
+ B) (A + C) = A + BC
Proof
(A + B) (A + C)
= AA + AC + AB + BC
= A + AC + AB + BC
= A (1 + C) + AB + BC
= A*1 + AB + BC
= A (1+ B) + BC
= A*1 + BC
=A + BC
ditulis oleh : Rani Yunita (2003015126)
sumber : https://onlinelearning.uhamka.ac.id
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