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If the resolution of a digital-to-analog converter is approximately 0.4% of its full-scale range, then it is a/an _______.
- a)16-bit converter
- b)10-bit converter
- c)8-bit converter
- d)12-bit converter
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
If the resolution of a digital-to-analog converter is approximately 0....
Concept of Resolution:
It is defined as the smallest change in the analog output voltage corresponding to a change of one bit in the digital output.
The percentage resolution (%R) of an n-bit DAC is:
Calculation:
As we know the formula resolution,
250 = 2N -1
2N = 251 ≈ 255
i.e., 28 = 255
N = 8
Hence the minimum value of N satisfying the condition.
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Community Answer
If the resolution of a digital-to-analog converter is approximately 0....
Explanation:
To understand why the correct answer is option 'C', let's break down the information given in the question.
Resolution of a digital-to-analog converter (DAC):
The resolution of a DAC refers to the smallest change in the analog output that can be achieved by the converter. It is often expressed as a percentage of the full-scale range of the DAC.
Full-scale range:
The full-scale range of a DAC is the maximum analog output voltage it can produce. It represents the range of values that can be represented by the digital input to the DAC.
Given information:
The resolution of the DAC is approximately 0.4% of its full-scale range. This means that the smallest change in the analog output is 0.4% of the full-scale range.
Relation between resolution and number of bits:
The resolution of a DAC is directly related to the number of bits it has. Each additional bit doubles the number of possible output values, which in turn reduces the size of the smallest change that can be achieved.
Calculating the number of bits:
To determine the number of bits of the DAC, we can use the formula:
Number of bits = log2 (Number of possible output values)
Since the resolution is approximately 0.4% of the full-scale range, the number of possible output values can be calculated as:
Number of possible output values = 100 / 0.4 = 250
Using the formula, we can calculate the number of bits:
Number of bits = log2 (250) ≈ 7.97
Rounded to the nearest whole number, the number of bits is 8. Therefore, the correct answer is option 'C' - an 8-bit converter.
To understand why the correct answer is option 'C', let's break down the information given in the question.
Resolution of a digital-to-analog converter (DAC):
The resolution of a DAC refers to the smallest change in the analog output that can be achieved by the converter. It is often expressed as a percentage of the full-scale range of the DAC.
Full-scale range:
The full-scale range of a DAC is the maximum analog output voltage it can produce. It represents the range of values that can be represented by the digital input to the DAC.
Given information:
The resolution of the DAC is approximately 0.4% of its full-scale range. This means that the smallest change in the analog output is 0.4% of the full-scale range.
Relation between resolution and number of bits:
The resolution of a DAC is directly related to the number of bits it has. Each additional bit doubles the number of possible output values, which in turn reduces the size of the smallest change that can be achieved.
Calculating the number of bits:
To determine the number of bits of the DAC, we can use the formula:
Number of bits = log2 (Number of possible output values)
Since the resolution is approximately 0.4% of the full-scale range, the number of possible output values can be calculated as:
Number of possible output values = 100 / 0.4 = 250
Using the formula, we can calculate the number of bits:
Number of bits = log2 (250) ≈ 7.97
Rounded to the nearest whole number, the number of bits is 8. Therefore, the correct answer is option 'C' - an 8-bit converter.
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