Boolean Expression From a Logic Circuit

Go to Math Operation

1) Read the circuit from inputs to output

Start at the input variables and follow each wire step by step until you reach the final output. Each logic gate represents an operation on the signals entering it.

2) Translate each gate

Use the gate type to write the matching boolean operation:

AND gives multiplication-like combination: both inputs must be true.
OR gives addition-like combination: at least one input must be true.
NOT gives the complement of a signal. If a gate has more than two inputs, combine all of them with the same operation.

3) Build the expression in order

Write the expression for each intermediate gate before moving to the next one. Add parentheses so the structure of the circuit stays clear. If the circuit has branches, write each branch separately, then combine them at the gate where they meet.

4) Simplify the final answer

After translating the whole circuit, simplify the expression using basic boolean rules such as removing repeated terms, eliminating double negations, and reducing expressions that are always true or false.

5) Check your result

Compare your simplified expression with the circuit behavior:

Test a few input combinations.
Make sure the output changes exactly as the circuit suggests.
Confirm that every inversion and gate connection was copied correctly.

A careful left-to-right translation and a final simplification usually gives the exact saved answer.