: Construct a truth table for a full adder circuit, again including the sum and carry-out outputs. Write the equation for each output that is minimal in terms of the number of gates required for implementation.

full adder is a digital circuit that performs the addition of three binary digits: the two bits to be added and a carry-in bit. The full adder has three inputs (A, B, and C) and two outputs (Sum and Carry-out). The truth table for a full adder is as follows:<br /><br />| A | B | C | Sum | Carry-out |<br />| --- | --- | --- | --- | --- |<br />| 0 | 0 | 0 | 0 | 0 |<br />| 0 | 0 | 1 | 1 | 0 |<br />| 0 | 1 | 0 | 1 | 0 |<br />| 0 | 1 | 1 | 0 | 1 |<br />| 1 | 0 | 0 | 1 | 0 |<br />| 1 | 0 | 1 | 0 | 1 |<br />| 1 | 1 | 0 | 0 | 1 |<br />| 1 | 1 | 1 | 1 | 0 |<br /><br />The equations for the Sum and Carry-out outputs in terms of the inputs A, B, and C are as follows:<br /><br />Sum = A XOR B XOR C<br />Carry-out = (A AND B) OR (C AND (A XOR B))<br /><br />These equations are minimal in terms of the number of gates required for implementation, as they can be implemented using only XOR, AND, and OR gates.