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 (Jawabanya)
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 (Jawabannya)
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 (Jawabannya)
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’ (Jawabannya)
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 (Jawabannya)
3. XZ
4. X + YZ
5. None of the above
6. Which of the following Boolean functions is algebraically complete?
1. F = xy (Jawabannya)
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’ (Jawabannya)
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 (Jawabannya)
9. An equivalent representation for the Boolean expression A' + 1 is
1. A
2. A’
3. 1 (Jawabannya)
4. 0
10. Simplification of the Boolean expression AB + ABC + ABCD + ABCDE + ABCDEF yields which of the following results?
1. ABCDEF
2.AB (Jawabannya)
3.AB +CD +EF
4. A+B+C+D+E+F
5.A+B(C+D(E+F))
1. HUKUM KOMUTATIF
a. A + B = B + A
| A | B | A + B | B + A |
| 0 0 1 1 | 0 1 0 1 | 0 1 1 1 | 0 1 1 1 |
b. A . B = B . A
| A | B | A . B | B . A |
| 0 0 1 1 | 0 1 0 1 | 0 0 0 1 | 0 0 0 1 |
2. HUKUM ASOSIATIF
a. (A + B) + C = A +(B + C)
| A | B | C | A + B | B + C | (A + B) + C | A + (B + C) |
| 0 0 0 0 1 1 1 1 | 0 0 1 1 0 0 1 1 | 0 1 0 1 0 1 0 1 | 0 0 1 1 1 1 1 1 | 0 1 1 1 0 1 1 1 | 0 1 1 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 | B . C | (A . B) . C | A . (B . C) |
| 0 0 0 0 1 1 1 1 | 0 0 1 1 0 0 1 1 | 0 1 0 1 0 1 0 1 | 0 0 0 0 0 0 1 1 | 0 0 0 1 0 0 0 1 | 0 0 0 0 0 0 0 1 | 0 0 0 0 0 0 0 1 |
3. HUKUM DISTRIBUTIF
a. A . (B + C) = A . B + A . C
| A | B | C | B + C | A . B | A . C | A.(B+C) | A.B + A.C |
| 0 0 0 0 1 1 1 1 | 0 0 1 1 0 0 1 1 | 0 1 0 1 0 1 0 1 | 0 1 1 1 0 1 1 1 | 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 0 1 1 1 |
b. A + (B . C) = (A + B)(A + C)
| A | B | C | B . C | A + B | A + C | A+(B.C) | (A+B)(A+C) |
| 0 0 0 0 1 1 1 1 | 0 0 1 1 0 0 1 1 | 0 1 0 1 0 1 0 1 | 0 0 0 1 0 0 0 1 | 0 0 1 1 1 1 1 1 | 0 1 0 1 1 1 1 1 | 0 0 0 1 1 1 1 1 | 0 0 0 1 1 1 1 1 |
4. HUKUM IDENTITY
a. A + A = A
| A + A | A |
| 0 0 1 1 | 0 0 1 1 |
b. A . A = A
| A . A | A |
| 0 0 1 1 | 0 0 1 1 |
5. a. A . B + A . B’ = A
| A | B | B’ | A . B | A . B’ | A.B + A.B’ |
| 0 0 1 1 | 0 1 0 1 | 1 0 1 0 | 0 0 0 1 | 0 0 1 0 | 0 0 1 1 |
b.(A +B)(A + B’) = A
| A | B | B’ | A + B | A + B’ | (A+B)(A+B’) |
| 0 0 1 1 | 0 1 0 1 | 1 0 1 0 | 0 1 1 1 | 1 0 1 1 | 0 0 1 1 |
6. HUKUM REDUDANSI
a. A + A . B = A
| A | B | A . B | A + A .B |
| 0 0 1 1 | 0 1 0 1 | 0 0 0 1 | 0 0 1 1 |
b. A (A + B) = A
| A | B | A + B | A (A+B) |
| 0 0 1 1 | 0 1 0 1 | 0 1 1 1 | 0 0 1 1 |
7. a. 0 + A = A
| A | 0 + A |
| 0 1 | 0 1 |
b.0 .A = 0
| A | 0 . A | 0 |
| 0 1 | 0 0 | 0 0 |
8. a. 1 + A = 1
| A | 1 + A | 1 |
| 0 1 | 0 0 | 1 1 |
b. 1 . A = A
| A | 1 . A |
| 0 1 | 0 1 |
9. a. A’ + A =1
| A | A’ | A’ + A | 1 |
| 0 1 | 1 0 | 1 1 | 1 1 |
b.A’ .A =0
| A | A’ | A’ . A | 0 |
| 0 1 | 1 0 | 0 0 | 0 0 |
10. a. A + A’ . B = A + B
| A | B | A’ | A’ . B | A + A’.B | A + B |
| 0 0 1 1 | 0 1 0 1 | 1 1 0 0 | 1 0 1 0 | 0 1 1 1 | 0 1 1 1 |
b.A(A’ +B) = A . B
| A | B | A’ | A’ + B | A (A’+B) | A . B |
| 0 0 1 1 | 0 1 0 1 | 1 1 0 0 | 1 1 0 1 | 0 0 0 1 | 0 0 0 1 |
11. THEOREMA DE MORGAN
a. (A + B)’ =A’ . B’
| A | B | A’ | B’ | A + B | (A +B)’ | A’ . B’ |
| 0 0 1 1 | 0 1 0 1 | 1 1 0 0 | 1 0 1 0 | 0 1 1 1 | 1 0 0 0 | 1 0 0 0 |
b. (A .B)’ = A’ + B’
| A | B | A’ | B’ | A . B | (A .B)’ | A’ + B’ |
| 0 0 1 1 | 0 1 0 1 | 1 1 0 0 | 1 0 1 0 | 0 0 0 1 | 1 1 1 0 | 1 1 1 0 |
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