4. Figure 3 shows a circuit for a digital-to-analog converter (DAC). The circuit accepts a4-bit input binary word a3a2a1ao, where ao, a1, a2, and a3 take the values of 0

or 1, and it provides an analog output voltage vo proportional to the value of the digital input. Each of the bits of the input word controls the correspondingly numbered switch. For instance,if a 2 is 0 then switch S2 connects the 20-kohms resistor to ground, while if az is 1 then S2connects the 20-k2 resistor to the +5-V power supply show that is vo given by v_{o}=-\frac{R_{f}}{16}\left[2^{0} a_{0}+2^{1} a_{1}+2^{2} a_{2}+2^{3} a_{3}\right] where Rf is in kilohms. Find the value of Rf so that vo ranges from 0 to-12 volts.