given the logic circuit diagram in figure 2.18, the boolean expression for y is:
To provide the Boolean expression for ( y ), I need more details about Figure 2.18 or information about the components in the logic circuit. Since you haven’t provided the actual circuit diagram, I’ll guide you on how to derive Boolean expressions from any logic circuit:
Steps to Write a Boolean Expression for Any Logic Circuit
-
Understand Inputs and Outputs:
- Identify all input variables (often named ( A, B, C, ) etc.) and note the output variable (e.g., ( Y )).
-
Label Intermediate Outputs:
- Break the circuit into stages and tag intermediate outputs for every gate. For example, label the output of the first gate as ( X_1 ), the next one as ( X_2 ), and so on.
-
Analyze Each Gate:
- Check the logic function of each gate:
- An AND gate combines inputs using multiplication (e.g., ( A \cdot B )).
- An OR gate combines inputs using addition (e.g., ( A + B )).
- A NOT gate inverts the input (e.g., ( \overline{A} )).
- Check the logic function of each gate:
-
Combine the Output and Derive ( Y ):
- Work step-by-step through the circuit, starting from the inputs to the final gate, and build the equation accordingly.
Example Circuit to Explain:
Let’s assume a generic logic circuit looks like this:
- ( A ) and ( B ) are inputs to an AND gate.
- The output of this AND gate is the input to an OR gate along with ( C ).
- The final OR gate produces the output ( Y ).
Boolean Expression Derivation for Y:
- Output of the AND gate = ( X_1 = A \cdot B )
- Inputs to the OR gate = ( X_1 ) and ( C ), so:
$$ Y = X_1 + C $$ - Substitute back ( X_1 = A \cdot B ):
$$ Y = (A \cdot B) + C $$
Thus, the Boolean expression for ( Y ) is:
$$ Y = (A \cdot B) + C $$
To Proceed with Your Circuit:
If you can describe Figure 2.18 or share details about the logic gates and their connections, I will give you the precise solution for your Boolean expression.