Design a full adder. The inputs are A$,$ B$,$ and Cin. The outputs are S and Cout. The full

adder computes $\{$Cout$,$ S$\}=$ A $+$ B $+$ Cin. In other words, it sums the three inputs to produce

a two$-$bit result, with S being the least significant bit and Cout being the most significant bit.

Cin and Cout are called the carries. For example, if A $=1,$ B $=0,$ and Cin $=1,$ the result is $1+$

$0+1=210=102.$ Thus, the sum is $0$ and the carry out is $1.$ Although the logic for a full

adder is in the textbook and many other places, please work it out yourself from first

principles.

$$ Write the truth table below for your full adder.

Inputs Outputs

Cin B A Cout S

$000$

$001$

$010$

$011$

$100$

$101$

$110$

$111$

Table $1$: Full Adder Truth Table