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
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))