Figure P2.43 shows a circuit for a digital-to-analog

Chapter 2, Problem 2.43

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Figure P2.43 shows a circuit for a digital-to-analog converter (DAC). The circuit accepts a 4-bit input binary word a3a2a1a0, where a0, 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 a2 is 0 then switch S2 connects the 20-k resistor to ground, while if a2 is 1 then S2 connects the 20-k resistor to the +5-V power supply. Show that vO is given bywhere Rf is in kilohms. Find the value of Rf so that vO ranges from 0 to 12 volts.

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