Tugas 4

Hukum Aljabar Boolean

T1. Hukum Komutatif

(a) A + B = B + A

Tabel Kebenaran:

A	B	A + B	B + A
0	0	0	0
0	1	1	1
1	0	1	1
1	1	1	1

(b) A B = B A

Tabel Kebenaran:

A	B	AB	BA
0	0	0	0
0	1	0	0
1	0	0	0
1	1	1	1

T2. Hukum Asosiatif

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

Tabel Kebenaran:

A	B	C	A + B	B + C	(A+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	0	1	0	1	1
1	0	1	1	1	1	1
1	1	0	1	1	1	1
1	1	1	1	1	1	1

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

Tabel Kebenaran:

A	B	C	AB	BC	(AB)C	A(BC)
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	1	0	0
1	0	0	0	0	0	0
1	0	1	0	0	0	0
1	1	0	1	0	0	0
1	1	1	1	1	1	1

T3. Hukum Distributif

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

Tabel Kebenaran:

A	B	C	B +C	AB	AC	A(B+C)	(AB)+(AC)
0	0	0	0	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
1	0	0	0	0	0	0	0
1	0	1	1	0	1	1	1
1	1	0	1	1	0	1	1
1	1	1	1	1	1	1	1

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

Tabel Kebenaran:

A	B	C	BC	A+B	A+C	A+(BC)	(A+B)(A+C)
0	0	0	0	0	0	0	0
0	0	1	0	0	1	0	0
0	1	0	0	1	0	0	0
0	1	1	1	1	1	1	1
1	0	0	0	1	1	1	1
1	0	1	0	1	1	1	1
1	1	0	0	1	1	1	1
1	1	1	1	1	1	1	1

T4. Hukum Identity

(a) A + A = A

Tabel Kebenaran:

A	A + A
0	0
0	0
1	1
1	1

(b) A A = A

Tabel Kebenaran:

A	A A
0	0
0	0
1	1
1	1

T5.

(a) AB + A B’

Tabel Kebenaran:

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

(b) (A+B)(A+B’)

Tabel Kebenaran:

A	B	B'	A+B	A+B'
0	0	1	0	1
0	1	0	1	0
1	0	1	1	1
1	1	0	1	1

T6. Hukum Redudansi

(a) A + A B = A

Tabel Kebenaran:

A	B	A B	A + A B
0	0	0	0
0	1	0	1
1	0	0	1
1	1	1	1

(b) A (A + B) = A

Tabel Kebenaran:

A	B	A + B	A (A + B)
0	0	0	0
0	1	1	0
1	0	1	1
1	1	1	1

T7

(a) 0 + A = A

Tabel Kebenaran:

A	0 + A
0	0
0	0
1	1
1	1

(b) 0 A = 0

Tabel Kebenaran:

A	0 A	0
0	0	0
0	0	0
1	0	0
1	0	0

T8

(a) 1 + A = 1

Tabel Kebenaran:

A	1 + A	1
0	1	1
0	1	1
1	1	1
1	1	1

(b) 1 A = A

Tabel Kebenaran:

A	1 A
0	0
0	0
1	1
1	1

T9

(a) A’ + A = 1

Tabel Kebenaran:

A	A'	A'	1
0	1	1	1
0	1	1	1
1	0	1	1
1	0	1	1

(b) A’ A=0

Tabel Kebenaran:

A	A'	A'A	0
0	1	0	0
0	1	0	0
1	0	0	0
1	0	0	0

T10

(a) A + A’ B =A + B

Tabel Kebenaran:

A	B	A'	A' B	A+B	A+A' B
0	0	1	1	0	0
0	1	1	0	1	1
1	0	0	1	1	1
1	1	0	0	1	1

(b) A (A’ + B) = AB

Tabel Kebenaran:

A	B	A'	A'+B	A B	A(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. TheoremaDe Morgan's

(a) (A’+B’)= A’B’

Tabel Kebenaran:

A	B	A'	B'	A+B	(A+B)'	A' B'
0	0	1	1	0	1	1
0	1	1	0	1	0	0
1	0	0	1	1	0	0
1	1	0	0	1	0	0

(b) (A’B’) = A’ + B’

Tabel Kebenaran:

A	B	A'	B'	A B	(AB)'	A'+B'
0	0	1	1	0	1	1
0	1	1	0	0	1	1
1	0	0	1	0	1	1
1	1	0	0	1	0	0

Quiz Aljabar Boolean

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
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
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
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'
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
3. XZ
4. X + YZ
5. None of the above

6. Which of the following Boolean functions is algebraically complete?
1. F = xy
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'
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

9. An equivalent representation for the Boolean expression A' + 1 is
1. A
2. A'
3. 1
4. 0

10. Simplification of the Boolean expression AB + ABC + ABCD + ABCDE + ABCDEF yields which of the following results?
1. ABCDEF
2. AB
3. AB + CD + EF
4. A + B + C + D + E + F
5. A + B(C+D(E+F))