Digital Electronics: Principles, Devices and Applications

Data Conversion Circuits – D/A and A/D Converters 483MostSignificantDigit(MSD)LeastSignificantDigit(LSD){D 1C 1B 1A 1{D 0C 0B 0A 0BCDD/AConverterAnalog O/PFigure 12.10BCD-input D/A converter.Example 12.1An eight-bit D/A converter has a step size of 20 mV. Determine the full-scale output and percentageresolution.Solution• (1/2 8 × V = 20 × 10 −3 , where V is the voltage corresponding to a logic ‘1’.• This gives V = 20 × 10 −3 × 2 8 = 5.12V.• The full-scale output = [(2 n − 1)/2 n ] × V = [(2 8 − 1)/2 8 ] × 5.12 = (255/256) × 5.12 = 5.1V.• The percentage resolution = [1/(2 n −1)] ×100 = 100/255 = 0392%.• The percentage resolution can also be determined from: (Step size/full-scale output) × 100 =(20 × 10 −3 /5.1) × 100 = 0.392 %.Example 12.2Refer to Fig. 12.11. This BCD D/A converter has a step size of 6.25 mV. Determine the full-scaleoutput.Solution• A step size of 6.25 mV implies that A 0 has a weight of 6.25 mV.• The weights of B 0 , C 0 and D 0 would respectively be 12.5, 25 and 50 mV.• Now, the weight of A 1 will be 10 times the weight of A 0 , i.e. the weight of A 1 will be 62.5 mV.• The weights of B 1 , C 1 and D 1 will accordingly be 125, 250 and 500 mV respectively.• On similar lines, the weights of A 2 , B 2 , C 2 and D 2 will respectively be 625 mV, 1.25 V, 2.5 V and5V.• For full-scale output, the input will be decimal 999. Each of the three four-bit groups will be 1001.• Therefore, the full-scale analogue output = 6.25 + 50 + 62.5 +500 + 625 + 5000 mV = 6.24375 V.• The full-scale analogue output can also be determined from the product of the step size and numberof steps. That is, the full-scale output = 6.25 × 999 = 6.24375 V.