1. **State the problem:** We have a 3-bit summing Digital-to-Analog Converter (DAC) with a binary input of 111 (binary), which equals 7 in decimal. 2. **Formula used:** The output voltage of an n-bit DAC with input digital value $D$ is given by: $$ V_{out} = V_{ref} \times \frac{D}{2^n - 1} $$ where $V_{ref}$ is the reference voltage, $D$ is the decimal equivalent of the binary input, and $n$ is the number of bits. 3. **Important rules:** - The maximum digital input for a 3-bit DAC is $2^3 - 1 = 7$. - The output voltage is proportional to the digital input. 4. **Calculate decimal value:** The binary input is 111, which is: $$ 1 \times 2^2 + 1 \times 2^1 + 1 \times 2^0 = 4 + 2 + 1 = 7 $$ 5. **Calculate output voltage:** Assuming the reference voltage $V_{ref}$ is known (let's denote it as $V_{ref}$), the output voltage is: $$ V_{out} = V_{ref} \times \frac{7}{7} = V_{ref} $$ 6. **Interpretation:** For the maximum input value 7, the output voltage equals the reference voltage. **Final answer:** $$ V_{out} = V_{ref} $$