195k views
5 votes
Simplify the following Boolean expressions to a minimum number of literals
xy+xy’

User Dsvensson
by
8.6k points

1 Answer

4 votes

Final answer:

To simplify the given Boolean expression xy+xy', we can eliminate the common term xy and use the distributive property to simplify it further.

Step-by-step explanation:

To simplify the given Boolean expression xy+xy', we can eliminate the common term xy. This leaves us with xy'+xy, which can be further simplified as xy+x(y'). Using the distributive property, we can simplify it to xy+xy', and since y+y' is always equal to 1, the final simplified expression is xy.

So, the simplified form of the Boolean expression xy+xy' is xy.

Example:

If x = true and y = false, then xy = true * false = false. Similarly, xy' = true * true = true. Therefore, xy+xy' = false + true = true, which matches the simplified expression xy.

To simplify the Boolean expression xy+xy', the common term xy is eliminated, resulting in xy'+xy. This is further simplified using the distributive property to xy+x(y'). Leveraging the fact that y+y' always equals 1, the final simplified expression is xy.

User Tikiboy
by
8.2k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories