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
b. A . A = A
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
b. 0 A = 0
T8.
a. 1 + A = 1
b. 1 A = A
T9.
a. A’ + A = 1
b. A’A = 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?
A * 1 = 1 A * 0 = 0 A + 0 = 0 A * A = A A * 1 = 1
2. Give the best definition of a literal?
A Boolean variable The complement of a Boolean variable 1 or 2 A Boolean variable interpreted literally 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
D + E A'B'C' D'E' 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'
x(x'y) = xy x*x' + y = xy x'(xy') = x'y' 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:
Z + YZ Z + XYZ XZ X + YZ None of the above
6. Which of the following Boolean functions is algebraically complete?
1. F = xy
F = x + y F = x' F = xy + yz F = x + y'
7. Simplification of the Boolean expression (A + B)'(C + D + E)' + (A + B)' yields which of the following results?
A + B A'B' C + D + E C'D'E' 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'?
F'= A+B+C+D+E F'= ABCDE F'= AB(C+D+E) F'= AB+C'+D'+E' F'= (A+B)CDE
9. An equivalent representation for the Boolean expression A' + 1 is
A A' 1 0
10. Simplification of the Boolean expression AB + ABC + ABCD + ABCDE + ABCDEF yields which of the following results?
ABCDEF AB AB + CD + EF A + B + C + D + E + F A + B(C+D(E+F))
