A Boolean expression is a mathematical expression that evaluates to either true or false. It is used to represent the logical relationship between two or more variables. In this article, we will discuss how to write a Boolean expression from a circuit.

A circuit is a physical representation of a Boolean expression. It consists of a set of logic gates, each of which performs a specific logical operation on its inputs. The output of each logic gate is then connected to the inputs of other logic gates, and so on. The final output of the circuit is the value of the Boolean expression.

To write a Boolean expression from a circuit, we need to first identify the logic gates and their inputs and outputs. We can then use the truth tables for each logic gate to determine the Boolean expression for the circuit.

For example, consider the following circuit:

This circuit consists of three logic gates: an AND gate, an OR gate, and a NOT gate. The inputs to the AND gate are A and B, the inputs to the OR gate are C and D, and the output of the NOT gate is E.

The truth table for the AND gate is as follows:

| A | B | Output | |---|---|---| | 0 | 0 | 0 | | 0 | 1 | 0 | | 1 | 0 | 0 | | 1 | 1 | 1 |

The truth table for the OR gate is as follows:

| A | B | Output | |---|---|---| | 0 | 0 | 0 | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 1 |

The truth table for the NOT gate is as follows:

| Input | Output | |---|---| | 0 | 1 | | 1 | 0 |

Using the truth tables for the logic gates, we can write the following Boolean expression for the circuit:

``` E = !(A && B) || (C && D) ```

This expression can be simplified to:

``` E = A'B' + C'D' ```

This is the Boolean expression for the circuit. It can be used to determine the output of the circuit for any given set of inputs.

Writing Boolean expressions from circuits is a useful skill for electrical engineers and computer scientists. It allows them to design and analyze circuits in a more efficient way.

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