Circuits to Truth Tables

Circuits are nothing but many logic gates connected together. Though these connections are made for accomplishing some specific goals like to add two or more integers or to shift a number leftwards by one bit but in the phase of understanding circuits, we can start with any random connection of logic gates. Following are examples of simple logical circuits.

There are some important rules to be followed for figuring out Truth Tables of such circuits. See the following:

• Identify all those connections in the circuit where output of some gate is going as input to some other gate. In all these connections mark intermediate output like F₁, F₂, F₃,.... F_n. Meanwhile ignore all the fresh inputs and final output.
• Draw truth table with only fresh inputs as inputs to the table and separate columns for different intermediate outputs. The very last column should be for final output.
• Based on the specific gates, deduce the intermediate outputs and keep on doing that till all intermediate outputs are not generated.
• Now the final output is easy to generate based on the gate used for creating it.

See the following example:

Here, F₁ is AND of A and B. Similarly F₂ is NOT of A. Now F₃ is OR of F₁ and F₂.