Tugas 4. Rangkuman Materi Aljabar Boolean

Rezha Ramadhan Pratama

1703015094

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

     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)

= 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

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