$26.$

Show that the circuit below functions as a DAC $($digital to analogue converter$)$ by calculating the output voltage $V_{\text{O}\text{u}\text{t}}$ as a function of $V_0$ and the switch settings $S_0,S_1,S_2,$ and $S_3($which can have a value of $0$ or $1).$

When $V_0=10V,$ what is the range of $V_{\text{o}\text{u}\text{r}}?$ Design a simple circuit to rescale the output to the range $0$ to $+5$ V