T1. Hukum Komutatif
a) A + B = B + A
Tabel Pembuktiannya :
| 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 Pembuktiannya :
| 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 )
Tabel Pembuktiaanya :
| 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 Pembuktiannya :
| A | B | C | A B | B C | ( A B ) C | A (B C) |
| 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 Pembuktiannya :
| A | B | C | B + C | A B | A C | 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 Pembuktiannya :
| A | B | C | B C | A + B | A + C | A + (B C) | (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 Pembuktiannya :
| A | A + A |
| 0 | 0 |
| 0 | 0 |
| 1 | 1 |
| 1 | 1 |
b) A A = A
Tabel Pembuktiannya :
| A | A A |
| 0 | 0 |
| 0 | 0 |
| 1 | 1 |
| 1 | 1 |
T5.
a) A B + A B'
Tabel Pembuktiannya :
| A | B | B’ | AB | AB’ | 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 Pembuktiannya :
| A | B | B’ | A + B | AB’ | ( A + B )( A + B’ ) |
| 0 | 0 | 1 | 0 | 1 | 0 |
| 0 | 1 | 0 | 1 | 0 | 0 |
| 1 | 0 | 1 | 1 | 1 | 1 |
| 1 | 1 | 0 | 1 | 1 | 1 |
T6. Hukum Redudansi
a) A + A B = A
Tabel Pembuktiannya :
| A | B | A + B | A (A + B) |
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 1 | 1 |
b) A (A + B) = A
Tabel Pembuktiannya :
| 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 Pembuktiannya :
| A | 0 + A |
| 0 | 0 |
| 0 | 0 |
| 1 | 1 |
| 1 | 1 |
b) 0 A = 0
Tabel Pembuktiannya :
| A | 0 A | 0 |
| 0 | 0 | 0 |
| 0 | 0 | 0 |
| 1 | 0 | 0 |
| 1 | 0 | 0 |
T8.
a) 1 + A = 1
Tabel Pembuktiannya :
| A | 1 + A | 1 |
| 0 | 1 | 1 |
| 0 | 1 | 1 |
| 1 | 1 | 1 |
| 1 | 1 | 1 |
b) 1 A = A
Tabel Pembuktiannya :
| A | 1 A |
| 0 | 0 |
| 0 | 0 |
| 1 | 1 |
| 1 | 1 |
T9
a) A’ + A = 1
Tabel Pembuktiannya :
| 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 Pembuktiannya :
| 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 Pembuktiannya :
| 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 Pembuktiannya :
| 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 Pembuktiannya :
| 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 Pembuktiannya :
| A | B | A’ | B’ | A B | (A B)’ | 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 |
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))
