2.7 Relating Logic Circuits To Boolean Expressions

In the previous discussion, we relate the Boolean expression with truth table, showing for each possible combination of input/output relationship in the form of a truth table. In this section, we will see the relationship of Boolean expression to logic circuit or vice-versa. Given the Boolean expression, we can get its equivalent logic circuit.

Part 2.7.1 Conversion from Boolean Expression to Logic Circuit.

To convert a Boolean expression to a logic circuit, follow these steps:

Step 1. Identify the variables: Determine the distinct variables present in the expression.

Step 2. Create a logic gate for each operation: Use logic gates (AND, OR, NOT, NAND, NOR, XOR, XNOR) to represent each Boolean operation in the expression.

Step 3. Connect the gates: Connect the input and output pins of the gates according to the order of operations in the expression.

Step 4. Label the inputs and outputs: Label the input pins with the corresponding variables and the output pin with the name of the expression.

Example no 1.

Convert F=ABC+BC’+AC’ to logic circuit.

Solution: 

Step 1. Identify the variables: Determine the distinct variables present in the expression.

Inputs: A, B, and C

Output: F

Step 2. Create a logic gate for each operation: Use logic gates (AND, OR, NOT, NAND, NOR, XOR, XNOR) to represent each Boolean operation in the expression.

Step 3. Connect the gates: Connect the input and output pins of the gates according to the order of operations in the expression.

Step 4. Label the inputs and outputs: Label the input pins with the corresponding variables and the output pin with the name of the expression.

Part 2.7.2 Conversion from Logic Circuit to Boolean Expression.

To convert a logic circuit to a Boolean expression, follow these steps:

Step 1. Identify the logic gates: Determine the types of logic gates (AND, OR, NOT, NAND, NOR, XOR, XNOR) used in the circuit.

Step 2. Label the inputs and outputs: Label the input and output pins of each gate with variables or expressions.

Step 3. Write Boolean expressions for each gate: Write the Boolean expression corresponding to each logic gate, using the labeled inputs and outputs.

Step 4. Combine expressions: Combine the expressions for the individual gates to form the overall Boolean expression for the circuit.

Example no 2.

Convert the Logic Circuit below to Boolean Expression.

Solution:

Our answer is F = ABC + AC’ + BC’.