Answer:
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 [tex]2^{12}[/tex] binary numbers, or 4096 positions. So to obtain the resolution in volts, is neccesary to divide the max input voltage in 4096.
[tex]2^{12}=4096\\ \\VFS=15v\\\\Voltage_step=\frac{VFS}{4096} =\frac{15}{4096}=0.0036 v[/tex]
Then Vin=6.83, so the output from the ADC is Vin/Voltage_step
[tex]ADC_{out} =\frac{V_{in} }{Voltagestep} =\frac{6.83}{0.00366} =1866[/tex]
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
[tex]011101001010_{2} =1866_{10} \\\\V_{out} =1866*0.00366=6.83 v[/tex]
