Hukum - Hukum Aljabar Boolean

Baik,,, buat semua yang ingin mengetahui tentang system digital. Dan ini adalah pengetahuan kamu tentang hukum aljabar Boolean.

Hukum – hokum Aljabar Boolean

T1. Hukum Komutatif.

a. 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

b. 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

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

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

T3. Hukum Distributif

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

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

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

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

T4. Hukum Identity

a. A + A = A

A	A + A	A
0	0	0
1	1	1

b. A . A = A

A	A . A	A
0	0	0
1	1	1

T5.

a. AB + AB’ = A

A	B	AB + AB’	A
0	0	0	0
0	1	0	0
1	0	1	1
1	1	1	1

b. ( A + B )( A + B’) = A

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

T6. Hukum Redudansi

a. A + A B = A

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

b. A (A + B) = A

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

T7.

a. 0 + A = A

A	0 + A	A
0	0	0
1	1	1

b. 0 A = 0

A	0 . A	0
0	0	0
1	0	0

T8.

a. 1 + A = 1

A	1 + A	1
0	1	1
1	1	1

b. 1 A = A

A	1 A	A
0	0	0
1	1	1

T9.

a. A’ + A = 1

A	A’ + A	1
0	1	1
1	1	1

b. A’A = 0

A	A’A	0
0	0	0
1	0	0

T10.

a. A + A’B = A + B

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

b. A ( A’ + B ) = AB

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

T11. Theorema De Morgan's

a. (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

b. (AB)’=A’+B

A	B	B’	B’	(AB)’	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

Quis 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))