CHAPTER 8. DATA ACQUISITION AND PROCESS CONTROL1678.7Problems1. Design an inverting op-amp circuit that has potentiometers for gain and oﬀset.2. Assuming that the diode shown in the circuit below exactly follows the equation I =I0(eV/VT− 1) with I0 =10−7 A and VT = 50 mV, sketch Vout versus Vin over the inputrange−2 V to +2 V. Show the scale on both axes.Vout10kohmVinFigure 8.10: Operational ampliﬁer with diode in feedback.3. Using two 1020-type DACs and two op-amps, design a circuit whose analog output isproportional to the product of two digital numbers.4. How many comparators are needed to build an 8-bit ﬂash encoder?5. Using a TDC, devise an experiment and show a complete block diagram of a laboratorysystem to determine the speed of a bullet.6. Consider the bad design of the synchronous counter shown below.CLOCKQ0Q3Q2Q1JCKSRQQJCKSRQQJCKSRQQJCKSRQQ(a) What must the JK inputs of the ﬁrst ﬂip-ﬂop be connected to for the circuit to“count”?(b) What must the SR inputs be connected to for the ﬂip-ﬂop output to be welldeﬁned?(c) Determine the truth table and decimal output for the synchronous counter.