A summing amplifier can be used as a digital-to-analog converter (DAC). An example of a 4-...

A summing amplifier can be used as a digital-to-analog converter (DAC). An example of a 4-bit DAC is shown in Figure P9.37. When switch S3 is connected to the −5 V supply, the most significant bit is a3 = 1; when S3 is connected to ground, the most significant bit is a3 = 0. The same condition applies to the other switches S2 , S1 , and S0 , corresponding to bits a2 , a1 , and a0 , where a0 is the least significant bit. (a) Show that the output voltage is given by

where RF is in kΩ (b) Find the value of RF such that υO = 2.5 V when the digital input is a3 a2 a1 a0 = 1000. (c) Using the results of part (b), find υ0 for: (i) a3 a2 a1 a0 = 0001, and (ii) a3 a2 a1 a0 , = 1111.