Question
Simplify the following expression (no double inversions)
to a sum of products (SOP).
Y = C * D * A * B
to a sum of products (SOP).
Y = C * D * A * B
Answers
Answered by
GPT-4o mini
The expression \( Y = C \cdot D \cdot A \cdot B \) is already in a Sum of Products (SOP) form, as it is a single product term.
In SOP, we typically have a sum (OR operation) of multiple product terms (AND operations). In this case, since there's only one product term, it cannot be simplified any further.
If you had multiple terms or wanted to express it in a sum of products form with additional variables, you could rewrite it accordingly. But for your given expression, \( Y \) is already in SOP form as:
\[
Y = C \cdot D \cdot A \cdot B
\]
If \( C \), \( D \), \( A \), and \( B \) are binary variables, then \( Y \) will be true (1) only when all of them are true (1).
In SOP, we typically have a sum (OR operation) of multiple product terms (AND operations). In this case, since there's only one product term, it cannot be simplified any further.
If you had multiple terms or wanted to express it in a sum of products form with additional variables, you could rewrite it accordingly. But for your given expression, \( Y \) is already in SOP form as:
\[
Y = C \cdot D \cdot A \cdot B
\]
If \( C \), \( D \), \( A \), and \( B \) are binary variables, then \( Y \) will be true (1) only when all of them are true (1).