Data Conversion Circuits – D/A and A/D Converters
483
BCD
D/A
Converter
{
D 1
C 1
B 1
A 1
{
D 0
C 0
B 0
A 0
Analog O/P
Most
Significant
Digit
(MSD)
Least
Significant
Digit
(LSD)
Figure 12.10 BCD-input D/A converter.
Example 12.1
An eight-bit D/A converter has a step size of 20 mV. Determine the full-scale output and percentage
resolution.
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 12.2
Refer to Fig. 12.11. This BCD D/A converter has a step size of 6.25 mV. Determine the full-scale
output.
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 and
5 V.
• 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 number
of steps. That is, the full-scale output = 6.25 × 999 = 6.24375 V.