COMPUTING

Digital−to−Analog ConvertersTABLE 5.1 Voltage levels for the circuit of Figure 5.81 and binary and decimal equivalentsVoltage Level Binary Equivalent Decimal EquivalentA B C DLOW LOW LOW LOW 0 0 0 0 0LOW LOW LOW HIGH 0 0 0 1 1LOW LOW HIGH LOW 0 0 1 0 2LOW LOW HIGH HIGH 0 0 1 1 3LOW HIGH LOW LOW 0 1 0 0 4LOW HIGH LOW HIGH 0 1 0 1 5LOW HIGH HIGH LOW 0 1 1 0 6LOW HIGH HIGH HIGH 0 1 1 1 7HIGH LOW LOW LOW 1 0 0 0 8HIGH LOW LOW HIGH 1 0 0 1 9HIGH LOW HIGH LOW 1 0 1 0 10HIGH LOW HIGH HIGH 1 0 1 1 11HIGH HIGH LOW LOW 1 1 0 0 12HIGH HIGH LOW HIGH 1 1 0 1 13HIGH HIGH HIGH LOW 1 1 1 0 14HIGH HIGH HIGH HIGH 1 1 1 1 15V D V C V B V AV D V AA digital−to−analog (D/A or DAC) converter is used to convert a binary output from a digital systemto an equivalent analog voltage. If there are 16 combinations of the voltages through , theanalog device should have 16 possible values. For example, since the binary number 1010 (decimal10) is twice the value of the binary number 0101 (decimal 5), an analog equivalent voltage of1010 must be double the analog voltage representing 0101.Figure 5.82 shows a DAC with binary−weighted resistors.R-----2 nR---8R---4R---2RV analogV NV DV CV BV AFigure 5.82. Digital−to−analog converter using binary−weighted resistorsWe can prove that the equivalent analog voltagethe relationV analogshown in Figure 5.82 is obtained fromVV A + 2V B + 4V C + 8V D + …analog= -----------------------------------------------------------------------------(5.71)1+ 2 + 4+ 8 + …The proof is left as an exercise at the end of this chapter.The DAC with binary−weighted resistors shown in Figure 5.82 has the disadvantage that itElectronic Devices and Amplifier Circuits with MATLAB Computing, Second EditionCopyright © Orchard Publications5−53