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.$$ Write the truth table below for your full adder. Inputs Outputs Cin B A Cout S$000001010011100101110111$Table $1$: Full Adder Truth Table$4$ Sketch a schematic using $74-$series components. Label each gate with the part number $($e$.$g$.04$ for a $74$HC$04$ inverter$)$ and label each gate$$s inputs and output with the pin number as described in Appendix