Tugas 5 [Fatih Zaidan Aqil] Aljabar Boolean

                                           Aturan – Aturan Aljabar Boolean

Commutative law of addition

Commutative law of addition, A+B = B+A the order of ORing does not matter.

Commutative law of Multiplication

Commutative law of Multiplication AB = BA the order of ANDing does not matter. 

Associative law of addition

Associative law of addition A + (B + C) = (A + B) + C The grouping of ORed 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 

- 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 LAW Program Studi T. Elektro FT - UHAMKA Slide - 4 17 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 output is 1 , If A is 0 the output is B Proof: A + AB = (A + AB) + AB RULE 10 Program Studi T. Elektro FT - UHAMKA Slide - 4 18 = (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

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