Multiple choice general knowledge science & technology

Simply the boolean function f=A.B.C.D + A.C.D + A.D

  1. A.D

  2. B.C

  3. A.B+C

  4. NONE OF THESE
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To simplify f = A.B.C.D + A.C.D + A.D, factor out A.D from all terms: f = A.D(B.C + C + 1). Since C + 1 = 1, and B.C + C = C(B + 1) = C, the expression reduces to A.D. This is a direct application of Boolean algebra factorization and identity laws.

AI explanation

To simplify the given Boolean function f = A.B.C.D + A.C.D + A.D, let's apply Boolean algebra and simplify each term:

f = A.B.C.D + A.C.D + A.D

First, let's factor out the common term 'A.D' from each term:

f = A.D(B.C + C + 1)

Now, let's simplify the expression (B.C + C + 1):

B.C + C + 1 = C(B + 1) + 1 = C + 1

Substituting this back into the original expression:

f = A.D(C + 1)

Now, we can see that the simplified form of the Boolean function f is A.D.

Therefore, the correct answer is A) A.D.

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