The given diagram is of a 4-bit switched current-source Digital to Analog Converter (DAC), where \( E_{REF} = 10V \) and \( R = 5 \, k\Omega \). What will be the output voltage \( V_{out} \) for the digital input 1101?
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To calculate the output of a DAC, use the formula \( V_{out} = E_{REF} \times \frac{D}{2^n - 1} \), where \( D \) is the decimal equivalent of the binary input, and \( n \) is the number of bits.
Step 1: Understanding the DAC.
The DAC converts a digital input to an analog voltage output. The digital input for a 4-bit DAC can range from \( 0000 \) to \( 1111 \), and the corresponding voltage is calculated based on the reference voltage \( E_{REF} \) and the resistors in the circuit.
Step 2: Calculating the output voltage.
For a 4-bit DAC, the output voltage is given by the formula:
\[
V_{out} = E_{REF} \times \left( \frac{D}{2^4 - 1} \right)
\]
where \( D \) is the decimal equivalent of the binary input. For the input 1101, the decimal equivalent is:
\[
D = 8 + 4 + 0 + 1 = 13
\]
Step 3: Substituting the values.
Now, substitute the values into the formula:
\[
V_{out} = 10V \times \left( \frac{13}{15} \right) = 8.125V
\]
Thus, the output voltage is \( 8.125V \), so the correct answer is (1).
