Question

simplify the boolean expression:X=ABC'D'+A'B'CD+AB'C'D+ABCD​

Answer 1

Answer:

X=A′B′C′D′+A′B′CD′+A′BCD′+ABCD′+AB′CD′

 

Here is what I did:

X===A′B′C′D′+A′CD′(B′+B)+ACD′(B+B′)A′B′C′D′+CD′(A′+A)D′(A′B′C′+C)

Explanation:

Answer 2

The simplified value X= ABC'D'+A'B'CD+AB'C'D+ABCD​ = AB'C'+CD(A'B'+AB).

Given,

The boolean expression, ABC'D'+A'B'CD+AB'C'D+ABCD​.

To Find,

The simplified version of this given boolean X.

Solution,

We can solve this boolean algebra problem using the following method.

The truth values, true and false, are generally labeled 1 and 0 respectively in Boolean algebra, which is a category of algebra in which the variable's values are the truth values, true and false.

It's a tool for analyzing and simplifying digital circuits or gates. It's also known as logical algebra or binary algebra.

ABC'D'+A'B'CD+AB'C'D+ABCD

=(AB'C'D+AB'C'D')+(A'B'CD+ABCD)

= AB'C'(D+D')+CD(A'B'+AB). . . . . . (i)

From Redundancy Laws we can say, (D+D')=1

(i)⇒

=AB'C'+CD(A'B'+AB).

Hence, The simplified value X= ABC'D'+A'B'CD+AB'C'D+ABCD​ = AB'C'+CD(A'B'+AB).

#SPJ3