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Circuit Diagram form of Boolean Expression

We can represent Boolean expression by circuit diagram and we can use circuit diagram for minimization.

Example 1: 

What is the logical expression of this circuit?

Logical expression of this circuit when the bulb is on: 

Example 2:

What is the logical expression of the circuit?

Logical expression of this circuit when the bulb is on: 

Question from GATE:

1. If a is connected to b then it is true (logic 1)

2. If a is connected to c then it is false (logic 0)

Logical expression for the bulb to be on

Solution: 

We get the bulb on when a is connected to b at S1, and at the same time a is connected to b at S2 OR when a is connected to c at S1 and at the same time a is connected to c at S2, in both cases circuit is going to closed and bulb on.

So, Boolean expression of the circuit when bulb on is: 

So, option (d) is the correct answer.

Another question of the same type as above:

The circuit diagram is a little different from the above question and the condition is the same.

1. If a is connected to b then it is true (logic 1)

2. If a is connected to c then it is false (logic 0)

Logical expression for the bulb to be on

Solution:

We get the bulb on, when a is connected to b at S1, and at the same time a is connected to c at S2 OR when a is connected to c at S1 and at the same time a is connected to bat S2, in both cases circuit is going to closed and bulb on.

So, Boolean expression of the circuit when bulb on is: 

So, option (c) is the correct answer.