Tugas 4

1. Pembuktian Rumus Bolean

TABEL BANTU
A	B	C	A'	B'	C'	B+C	B.C	A.B'	A+B'	A.C	A+C	A'.B	A'+B	(A+B)'	(A.B)'
1	1	1	0	0	0	1	1	0	1	1	1	0	1	0	0
1	1	0	0	0	1	1	0	0	1	0	1	0	1	0	0
1	0	1	0	1	0	1	0	1	1	1	1	0	0	0	1
1	0	0	0	1	1	0	0	1	1	0	1	0	0	0	1
0	1	1	1	0	0	1	1	0	0	0	1	1	1	0	1
0	1	0	1	0	1	1	0	0	0	0	0	1	1	0	1
0	0	1	1	1	0	1	0	0	1	0	1	0	1	1	1
0	0	0	1	1	1	0	0	0	1	0	0	0	1	1	1

Hukum Komulatif								Hukum Asosiatif
A+B			B+A		A.B		B.A	(A+B)+C		A+(B+C)	(A.B).C	A.(B.C)
1			1		1		1	1		1	1	1
1			1		1		1	1		1	0	0
1			1		0		0	1		1	0	0
1			1		0		0	1		1	0	0
1			1		0		0	1		1	0	0
1			1		0		0	1		1	0	0
0			0		0		0	1		1	0	0
0			0		0		0	0		0	0	0
Hukum Identity
A+A	A	A.A		A.B+A.B'		(A+B).(A+B')
1	1	1		1		1
1	1	1		1		1
1	1	1		1		1
1	1	1		1		1
0	0	0		0		0
0	0	0		0		0
0	0	0		0		0
0	0	0		0		0

Hukum Distributif
A.(B+C)	A.B+A.C	A+(B.C)	(A+B)(A+C)
1	1	1	1
1	1	1	1
1	1	1	1
0	0	1	1
0	0	1	1
0	0	0	0
0	0	0	0
0	0	0	0

Hukum Redudansi
A+A.B	A.(A+B)	A	0+A	0.A	1+A	1.A	A+A'	A.A'
1	1	1	1	0	1	1	1	0
1	1	1	1	0	1	1	1	0
1	1	1	1	0	1	1	1	0
1	1	1	1	0	1	1	1	0
0	0	0	0	0	1	0	1	0
0	0	0	0	0	1	0	1	0
0	0	0	0	0	1	0	1	0
0	0	0	0	0	1	0	1	0

				Theoroma De Morgan
A+A'B	A+B	A(A'+B)	A.B	(A+B)'	A'.B'	(A.B)'	A'+B'
1	1	1	1	0	0	0	0
1	1	1	1	0	0	0	0
1	1	0	0	0	0	1	1
1	1	0	0	0	0	1	1
1	1	0	0	0	0	1	1
1	1	0	0	0	0	1	1
0	0	0	0	1	1	1	1
0	0	0	0	1	1	1	1

2. 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

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))