Question
Simplify the following expression (no double inversions)
to a sum of products (SOP).
Y = C * D * A * B
A and B have line on top inside of C and D
C and D have line on top of whole letters
to a sum of products (SOP).
Y = C * D * A * B
A and B have line on top inside of C and D
C and D have line on top of whole letters
Answers
Answered by
GPT-4o mini
In order to simplify the expression \( Y = C \cdot D \cdot A \cdot B \) given that \( A \) and \( B \) have a line (negation) on top (which typically indicates NOT), and that \( C \) and \( D \) also have a line on top (indicating NOT), we can denote negations as follows:
- \( A' \) represents NOT A (A with a line on top)
- \( B' \) represents NOT B (B with a line on top)
- \( C' \) represents NOT C (C with a line on top)
- \( D' \) represents NOT D (D with a line on top)
Now the expression can be rewritten in terms of those negated variables:
\[
Y = C' \cdot D' \cdot A' \cdot B'
\]
Given that the product of two negations doesn't alter the state beyond being the product of the variables, and all negations are involved in the products, we leave the expression in the form stated.
Thus, the simplified expression in Sum of Products (SOP) form is:
\[
Y = C' \cdot D' \cdot A' \cdot B'
\]
This is already expressed in a product format, and since there are no additional factors to combine further or simplify, this is indeed the sum of products representation for the provided variables.
- \( A' \) represents NOT A (A with a line on top)
- \( B' \) represents NOT B (B with a line on top)
- \( C' \) represents NOT C (C with a line on top)
- \( D' \) represents NOT D (D with a line on top)
Now the expression can be rewritten in terms of those negated variables:
\[
Y = C' \cdot D' \cdot A' \cdot B'
\]
Given that the product of two negations doesn't alter the state beyond being the product of the variables, and all negations are involved in the products, we leave the expression in the form stated.
Thus, the simplified expression in Sum of Products (SOP) form is:
\[
Y = C' \cdot D' \cdot A' \cdot B'
\]
This is already expressed in a product format, and since there are no additional factors to combine further or simplify, this is indeed the sum of products representation for the provided variables.