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A sensor needs a bias voltage of +3.000 volts. The DAC producing the voltage is 12 bits with a 3.3 volt reference. What is the DAC input code? 1241 3724 3103 3541

A sensor needs a bias voltage of +3.000 volts. The DAC producing the voltage is 12 bits with a 3.3 volt reference. What is the DAC input code? 1241 3724 3103 3541

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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**Question:** A sensor needs a bias voltage of +3.000 volts. The DAC producing the voltage is 12 bits with a 3.3 volt reference. What is the DAC input code? - ○ 1241 - ○ 3724 - ○ 3103 - ○ 3541 **Explanation:** To find the correct DAC input code, use the formula for a Digital-to-Analog Converter (DAC): \[ \text{Output Voltage} = \left(\frac{\text{Digital Code}}{2^n - 1}\right) \times \text{Reference Voltage} \] Where: - \( n \) is the number of bits (12 bits in this case). - Digital Code is what we are trying to find. - Reference Voltage is 3.3 volts. Rearranging for the Digital Code gives: \[ \text{Digital Code} = \left(\frac{\text{Output Voltage} \times (2^n - 1)}{\text{Reference Voltage}}\right) \] Plug in the values: \[ \text{Digital Code} = \left(\frac{3.000 \times (2^{12} - 1)}{3.3}\right) \] Calculate: \[ 2^{12} - 1 = 4095 \] \[ \text{Digital Code} = \left(\frac{3.000 \times 4095}{3.3}\right) \] \[ \text{Digital Code} \approx 3724 \] Therefore, the correct answer is: - ○ 3724
Transcribed Image Text:**Question:** A sensor needs a bias voltage of +3.000 volts. The DAC producing the voltage is 12 bits with a 3.3 volt reference. What is the DAC input code? - ○ 1241 - ○ 3724 - ○ 3103 - ○ 3541 **Explanation:** To find the correct DAC input code, use the formula for a Digital-to-Analog Converter (DAC): \[ \text{Output Voltage} = \left(\frac{\text{Digital Code}}{2^n - 1}\right) \times \text{Reference Voltage} \] Where: - \( n \) is the number of bits (12 bits in this case). - Digital Code is what we are trying to find. - Reference Voltage is 3.3 volts. Rearranging for the Digital Code gives: \[ \text{Digital Code} = \left(\frac{\text{Output Voltage} \times (2^n - 1)}{\text{Reference Voltage}}\right) \] Plug in the values: \[ \text{Digital Code} = \left(\frac{3.000 \times (2^{12} - 1)}{3.3}\right) \] Calculate: \[ 2^{12} - 1 = 4095 \] \[ \text{Digital Code} = \left(\frac{3.000 \times 4095}{3.3}\right) \] \[ \text{Digital Code} \approx 3724 \] Therefore, the correct answer is: - ○ 3724
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