Question

Find d from the logic circuit shown below. Create a logical expression for the circuit.

Answer 1

The output 'd' of the logic circuit is 0, and the logical expression representing the behavior of the circuit is:
`\( d = (\overline{a} \cdot b) + (\overline{c} \cdot \overline{d}) \)`.

Step-by-step explanation:

Analyzing the logic circuit, 'd' is determined by two main logical operations: an AND gate involving the complement of 'a' and 'b'
`(\(\overline{a} \cdot b\))` and an OR gate involving the complements of 'c' and 'd'
`(\(\overline{c} \cdot \overline{d}\))`. The AND gate condition results in 'd' being 0 when 'a' is 0 and 'b' is 1. The OR gate condition contributes to 'd' being 0 when both 'c' and 'd' are 1. Combining these conditions, 'd' equals 0 under the given circumstances.

The logical expression
`\( d = (\overline{a} \cdot b) + (\overline{c} \cdot \overline{d}) \)` captures the behavior of the circuit. It specifies that 'd' is determined by the OR combination of two AND conditions: the first involving the complement of 'a' and 'b' and the second involving the complements of 'c' and 'd'. This expression accurately represents the conditions necessary for 'd' to output a value of 0.

Here is complete question;

"Examine the given logic circuit and determine the output, denoted as 'd.' Additionally, articulate a logical expression that represents the behavior of the circuit in terms of its input variables."