Final answer:
A full adder is a combinational digital circuit used for binary addition, employing a decoder to simplify its implementation. The truth table illustrates the possible input-output combinations, with SOP expressions derived for sum and carry outputs. These expressions are then implemented through a decoder and OR gates to achieve the necessary logic.
Step-by-step explanation:
Introduction to Full Adder Circuit using a Decoder
A full adder is a digital circuit that computes the addition of three binary bits. It has three inputs - two significant bits and one previous carry bit - and two outputs, the sum and the carry-out. Using a decoder in the design of a full adder allows for the implementation of the full adder's logic function through a set of combinational logic gates dictated by the decoder's output.
Full Adder Truth Table
... rest of the truth table ...
ABCinSumCout00000
From the truth table, we can derive the Sum and Carry out expressions using the Sum of Products (SOP) method for the outputs.
SOP Expression
Sum = AB'Cin' + A'BCin' + A'B'Cin + ABCin
Cout = AB + ACin + BCin
Circuit Implementation with Decoder
The decoder can be used as the foundation for the full adder circuit. The SOP expressions we derived can be mapped to the outputs of the decoder. Each output corresponds to one minterm of the SOP expression. The final step is to connect these outputs through OR gates to generate the Sum and Carry-out signals.