$10\mathrm{.}70.$ The summing amplifier can be used as a digitally controlled volume control using the circuit in Fig. P$10\mathrm{.}70.$ The individual bits of the $4-$bit binary input word $(b_1{b}_2{b}_3{b}_4)$ are used to control the position of the switches with the resistor connected to $0V$ if $b_i=0$ and connected to the input signal $v_l$ if $b_i=1.($a$)$ What is the output voltage $v_0$ with the data input $0110$ if $v_{\text{I}}=2sin4000t$ V$?($b$)$ Suppose the input changes to $1011.$ What will be the

new output voltage? $($c$)$ Make a table giving the output voltages for all $16$ possible input combinations.

Figure $P10\mathrm{.}70$