Minggu, 18 April 2010

tugas 4 ( hukum aljabar)

Soal :


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

1. A * 1 = 1

2. A * 0 = 0 (Jawabanya)

3. A + 0 = 0

4. A * A = A

5. A * 1 = 1


2. Give the best definition of a literal?

1. A Boolean variable

2. The complement of a Boolean variable (Jawabannya)

3. 1 or 2

4. A Boolean variable interpreted literally

5. The actual understanding of a Boolean variable


3. Simplify the Boolean expression (A+B+C)(D+E)' + (A+B+C)(D+E) and choose the best answer.

1. A + B + C (Jawabannya)

2. D + E

3. A’B’C’

4. D’E’

5. None of the above


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

1. x’(x+y’) = x’y’ (Jawabannya)

2 x(x’y) = xy

3. x*x’ + y = xy

4. x’(xy’) = x’y’

5. x(x’ + y) = xy


5.Given the function F(X,Y,Z) = XZ + Z(X'+ XY), the equivalent most simplified Boolean representation for F is:

1. Z + YZ

2. Z + XYZ (Jawabannya)

3. XZ

4. X + YZ

5. None of the above


6. Which of the following Boolean functions is algebraically complete?

1. F = xy (Jawabannya)

2. F = x + y

3. F = x’

4. F = xy +yz

5. F = x + y’


7. Simplification of the Boolean expression (A + B)'(C + D + E)' + (A + B)' yields which of the following results?

1. A + B

2. A’B’ (Jawabannya)

3. C + D + E

4. C’D’E’

5. A’B’C’D’E’



8. Given that F = A'B'+ C'+ D'+ E', which of the following represent the only correct expression for F'?

1. F’= A+B+C+D+E

2. F’= ABCDE

3. F’= AB(C+D+E)

4. F’= AB+C’+D’+E’

5. F’= (A+B)CDE (Jawabannya)


9. An equivalent representation for the Boolean expression A' + 1 is

1. A

2. A’

3. 1 (Jawabannya)

4. 0


10. Simplification of the Boolean expression AB + ABC + ABCD + ABCDE + ABCDEF yields which of the following results?

1. ABCDEF

2.AB (Jawabannya)

3.AB +CD +EF

4. A+B+C+D+E+F

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


Hukum Aljabar Boolean


1. HUKUM KOMUTATIF


a. A + B = B + A

A

B

A + B

B + A

0

0

1

1

0

1

0

1

0

1

1

1

0

1

1

1


b. A . B = B . A

A

B

A . B

B . A

0

0

1

1

0

1

0

1

0

0

0

1

0

0

0

1


2. HUKUM ASOSIATIF


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

A

B

C

A + B

B + C

(A + B) + C

A + (B + C)

0

0

0

0

1

1

1

1

0

0

1

1

0

0

1

1

0

1

0

1

0

1

0

1

0

0

1

1

1

1

1

1

0

1

1

1

0

1

1

1

0

1

1

1

1

1

1

1

0

1

1

1

1

1

1

1


b. (A . B) . C = A . (B . C)

A

B

C

A . B

B . C

(A . B) . C

A . (B . C)

0

0

0

0

1

1

1

1

0

0

1

1

0

0

1

1

0

1

0

1

0

1

0

1

0

0

0

0

0

0

1

1

0

0

0

1

0

0

0

1

0

0

0

0

0

0

0

1

0

0

0

0

0

0

0

1


3. HUKUM DISTRIBUTIF

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

A

B

C

B + C

A . B

A . C

A.(B+C)

A.B + A.C

0

0

0

0

1

1

1

1

0

0

1

1

0

0

1

1

0

1

0

1

0

1

0

1

0

1

1

1

0

1

1

1

0

0

0

0

0

0

1

1

0

0

0

0

0

1

0

1

0

0

0

0

0

1

1

1

0

0

0

0

0

1

1

1


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

A

B

C

B . C

A + B

A + C

A+(B.C)

(A+B)(A+C)

0

0

0

0

1

1

1

1

0

0

1

1

0

0

1

1

0

1

0

1

0

1

0

1

0

0

0

1

0

0

0

1

0

0

1

1

1

1

1

1

0

1

0

1

1

1

1

1

0

0

0

1

1

1

1

1

0

0

0

1

1

1

1

1


4. HUKUM IDENTITY


a. A + A = A

A + A

A

0

0

1

1

0

0

1

1


b. A . A = A

A . A

A

0

0

1

1

0

0

1

1



5. a. A . B + A . B’ = A

A

B

B’

A . B

A . B’

A.B + A.B’

0

0

1

1

0

1

0

1

1

0

1

0

0

0

0

1

0

0

1

0

0

0

1

1


b.(A +B)(A + B’) = A

A

B

B’

A + B

A + B’

(A+B)(A+B’)

0

0

1

1

0

1

0

1

1

0

1

0

0

1

1

1

1

0

1

1

0

0

1

1


6. HUKUM REDUDANSI


a. A + A . B = A

A

B

A . B

A + A .B

0

0

1

1

0

1

0

1

0

0

0

1

0

0

1

1


b. A (A + B) = A

A

B

A + B

A (A+B)

0

0

1

1

0

1

0

1

0

1

1

1

0

0

1

1



7. a. 0 + A = A

A

0 + A

0

1

0

1


b.0 .A = 0

A

0 . A

0

0

1

0

0

0

0



8. a. 1 + A = 1

A

1 + A

1

0

1

0

0

1

1


b. 1 . A = A

A

1 . A

0

1

0

1



9. a. A’ + A =1

A

A’

A’ + A

1

0

1

1

0

1

1

1

1


b.A’ .A =0

A

A’

A’ . A

0

0

1

1

0

0

0

0

0




10. a. A + A’ . B = A + B

A

B

A’

A’ . B

A + A’.B

A + B

0

0

1

1

0

1

0

1

1

1

0

0

1

0

1

0

0

1

1

1

0

1

1

1


b.A(A’ +B) = A . B

A

B

A’

A’ + B

A (A’+B)

A . B

0

0

1

1

0

1

0

1

1

1

0

0

1

1

0

1

0

0

0

1

0

0

0

1


11. THEOREMA DE MORGAN


a. (A + B)’ =A’ . B’

A

B

A’

B’

A + B

(A +B)’

A’ . B’

0

0

1

1

0

1

0

1

1

1

0

0

1

0

1

0

0

1

1

1

1

0

0

0

1

0

0

0


b. (A .B)’ = A’ + B’

A

B

A’

B’

A . B

(A .B)’

A’ + B’

0

0

1

1

0

1

0

1

1

1

0

0

1

0

1

0

0

0

0

1

1

1

1

0

1

1

1

0