Selasa, 20 April 2010

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TUGAS 4 A

HUKUM KOMUTATIF

1. A + B = B + A

  

A

B

A+B

B+A

0

0

0

0

0

1

1

1

1

0

1

1

1

1

1

1

2. A . B = B . A

  

A

B

A B

B A

0

0

0

0

0

1

0

0

1

0

0

0

1

1

1

1


 

T2. HUKUM ASOSIATIF

1. (A + B) + C = A + (B + C)

   

A

B

C

A+B

(A+B)+C

B+C

A+(B+C)

0

0

0

0

0

0

0

0

0

1

0

1

1

1

0

1

0

1

1

1

1

0

1

1

1

1

1

1

1

0

1

1

1

1

1

1

1

1

1

1

1

1

2. (A B) C = A (B C)

    

A

B

C

A B

(A . B) C

B C

A (B . C)

0

0

0

0

0

0

0

0

0

1

0

0

0

0

0

1

0

0

0

0

0

0

1

1

0

0

1

0

1

0

1

0

0

0

0

1

1

1

1

1

1

1


 

T3. HUKUM DISTRIBUTIF

     

1.
A (B + C) = A . B + A

    

A

B

C

B+C

A (B+C)

A . B

A . B + A

 

0

0

0

0

0

0

0

 

0

0

1

1

0

0

0

 

0

1

0

1

0

0

0

 

0

1

1

1

0

0

0

 

1

0

1

1

1

0

1

 

1

1

1

1

1

1

1

 

2.
A + (B . C) = (A + B) (A + C)

   

A

B

C

B . C

A+ (B . C)

A+B

A+C

(A+B)(A+C)

0

0

0

0

0

0

0

0

0

0

1

0

0

0

1

0

0

1

0

0

0

1

0

0

0

1

1

1

1

1

1

1

1

0

1

0

1

1

1

1

1

1

1

1

1

1

1

1


 

T4. HUKUM IDENTITY

1.
A + A = A

 

A

A+A

 

0

0

 

1

1

 

2. A A = A

 

A

A . A

 

0

0

 

1

1

 


 

T5.

     

1. A . B + A . B' = A

   

A

B

B'

A B

A B'

AB+AB'

0

0

1

0

0

0

0

1

0

0

0

0

1

0

1

0

1

1

1

1

0

1

0

1

2. (A+B) (A+B') = A

   

A

B

B'

A+B

A+B'

(A+B)(A+B')

0

0

1

0

1

0

0

1

0

1

0

0

1

0

1

1

1

1

1

1

0

1

1

1


 

T6. HUKUM REDUDANSI

 

1.
A + A . B = A

 

A

B

A . B

A+AB

0

0

0

0

0

1

0

0

1

0

0

1

1

1

1

1

2.
A (A + B) = A

 

A

B

A+B

A(A+B)

0

0

0

0

0

1

1

0

1

0

1

1

1

1

1

1


 

T7.

  

1. 0 + A = A

A

  

0+A

0

0

0

1

0

1

2. 0 . A = 0

A

  

  

0

0

0

1

0

0


 

T8.

  

1. 1 + A = 1

A

  

1+A

0

1

1

1

1

1

2. 1 . A = A

A

  

  

0

1

0

1

1

1


 

T9.

  

1. A' + A = 1

A

A'

A'+A

0

1

1

1

0

1

2. A' A = 0

A

A'

A' A

0

1

0

1

0

0


 

T10.

     

1. A + A' B = A + B

A

B

A'

A' B

A+A'B

A+B

0

0

1

0

0

0

0

1

1

1

1

1

1

0

0

0

1

1

1

1

0

0

1

1

2. A ( A' + B) = A B

A

B

'A'

A'+B

A(A'+B)

A . B

0

0

1

1

0

0

0

1

1

1

0

0

1

0

0

0

0

0

1

1

0

1

1

1


 

T11.THEOREMA De MORGAN'S

   

1.
( A + B)' = A' B'

A

B

A'

B'

(A+B)'

A' . B'

0

0

1

1

1

1

0

1

1

0

0

0

1

0

0

1

0

0

1

1

0

0

0

0

2.
( A B )' = A' + B'

A

B

A'

B'

(A . B)'

A'+B'

0

0

1

1

1

1

0

1

1

0

1

1

1

0

0

1

1

1

1

1

0

0

0

0


 


 

TUGAS 4 B


 

  1. Give the relationship that represents the dual of the Boolean property A + 1 = 1?
    (Note: * = AND, + = OR and ' = NOT)

    A * 1 = 1

    A * 0 = 0

    A + 0 = 0

    A * A = A

    A * 1 = 1

  2. A Boolean variable

    The complement of a Boolean variable

    1 or 2

    A Boolean variable interpreted literally

    The actual understanding of a Boolean variable

  3. A + B + C

    D + E

    A'B'C'

    D'E'

  4. Which of the following relationships represents the dual of the Boolean property x + x'y = x + y?

    x'(x + y') = x'y'

    x(x'y) = xy

    x*x' + y = xy

    x'(xy') = x'y'

    x(x' + y) = xy

  5. Z + YZ

    Z + XYZ

    XZ

    X + YZ

    None of the above

  6. F = xy

    F = x + y

    F = x'

    F = xy + yz

    F = x + y'

  7. A + B

    A'B'

    C + D + E

    C'D'E'

    A'B'C'D'E'

  8. F'= A+B+C+D+E

    F'= ABCDE

    F'= AB(C+D+E)

    F'= AB+C'+D'+E'

    F'= (A+B)CDE


     

  9. A

    A'

    1

    0

  10. ABCDEF

    AB

    AB + CD + EF

    A + B + C + D + E + F

    A + B(C+D(E+F))


 

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