Hello can somebody help me? How this boolean expression simplified?
abcd + d
it simplified as:
d
im trying to use the Laws I don't understand at all
Here's the Laws
Basic Boolean Laws
Idempotent Law
A * A = A
A + A = A
Associative Law
(A * B) * C = A * (B * C)
(A + B) + C = A + (B + C)
Commutative Law
A * B = B * A
A + B = B + A
Distributive Law
A * (B + C) = A * B + A * C
A + (B * C) = (A + B) * (A + C)
Identity Law
A * 0 = 0 A * 1 = A
A + 1 = 1 A + 0 = A
Complement Law
A * ~A = 0
A + ~A = 1
Involution Law
~(~A) = A
DeMorgan's Law
~(A * B) = ~A + ~B
~(A + B) = ~A * ~B
Redundancy Laws
Absorption
A + (A * B) = A
A * (A + B) = A
(A * B) + (A * ~B) = A
(A + B) * (A + ~B) = A
A + (~A * B) = A + B
A * (~A + B) = A * B
Thanks in advance!
It's indeed D, by the following:
abcd+d -> (a+d)*(b+d)*(c+d)*(d+d) // Distributive Law
(a+d)*(b+d)*(c+d)*(d+d) -> (a+d)*(b+d)*(c+d)*d // Idempotent Law - d+d=d
(a+d)*(b+d)*(c+d)*d -> (a+d)*(b+d)*d // Redundancy Laws - (c+d)*d = d
(a+d)*(b+d)*d -> (a+d)*d // Redundancy Laws - (b+d)*d = d
(a+d)*d -> d // Redundancy Laws - (a+d)*d = d