Consider a digital system where an input voltage vin is converted to digital with an adc, the output of which is converted back to an analog output voltage vout with a dac. bit resolution n=12, vfs=15v,
find vout for vin=6.83v

Vout=6.83 v

Explanation:

The resolution steps are going to be from 0.00366 V from the DAC and from the ADC, with 12 bits resolution and VFS =15v

Because, 12 bits resolution means binary numbers, or 4096 positions. So to obtain the resolution in volts, is neccesary to divide the max input voltage in 4096.

Then Vin=6.83, so the output from the ADC is Vin/Voltage_step

in base 2: ADC out= 011101001010

Now, this is the same DAC input= 011101001010

And to calculate the output we multiply by the same resolution step

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