A one-bit full adder is to be implemented using $8$-to-$1$ multiplexers $\text{(MUX)}$.
- Write the truth table for sum $\text{(S)}$ and carry to the next stage $\left(\mathrm{C}_{\mathrm{N}}\right)$ in terms of the two bits $\text{(A, B)}$ and carry from the previous stage $\left(\text{C}_{p}\right)$, The truth table should be in the ascending order of $\left(\mathrm{A}, \mathrm{B}, \mathrm{C}_{p}\right)$, i.e. $(000,001,010$, ... etc.).
- Implement $\text{S}$ and $\text{C}_{N}$ using $8$-to-$1$ multiplexers.