A four-bit R-2R ladder DAC is presented in Fig. 5.103.
(a) Show that the output voltage is given by
-V_{o}=R_{f}\left(\frac{V_{1}}{2 R}+\frac{V_{2}}{4 R}+\frac{V_{3}}{8 R}+\frac{V_{4}}{16 R}\right.)
(b) If { R }_{ f } = 12 kΩ and R = 10 kΩ, find |{ V }_{0 } | for [{ V }_{ 1 } { V }_{ 2 } { V }_{ 3 } { V }_{ 4 }] = [1011] and [{ V }_{ 1 } { V }_{ 2 } { V }_{ 3 } { V }_{ 4 }] = [0101].