Binary-weighted DAC (operational-amplifier summing type): Evaluate the statement — “In a binary-weighted digital-to-analog converter, the sum of all currents from the binary-weighted resistors flows through the operational amplifier.” Clarify where these currents actually go in the classic inverting-summing DAC topology and state whether the claim is valid.

Introduction / Context:
A binary-weighted digital-to-analog converter (DAC) commonly uses an operational amplifier as an inverting summing amplifier. Understanding the exact current paths in this topology is essential for correct intuition about linearity, settling, and output scaling. The statement claims that the summed current “flows through the operational amplifier,” which is a frequent misconception.

Given Data / Assumptions:

• Classic inverting DAC: binary-weighted resistors feed an op-amp summing node.
• Ideal op-amp assumptions: infinite input impedance, virtual ground at the inverting input, and zero input current.
• Feedback element (usually a resistor, sometimes a capacitor for filtering) from output to the inverting node.

Concept / Approach:
In an ideal op-amp, the inverting input is a virtual ground that draws negligible current. Currents from the binary-weighted network meet at the summing node and must continue through the feedback path to the output node, not into the op-amp input. Therefore, the op-amp enforces node voltage (virtual ground) and provides output current via its output stage, but the input terminal itself does not carry the summed current.

Step-by-Step Solution:
1) Binary-weighted sources produce currents I1, I2, … determined by input bits and resistor values.2) These currents enter the inverting summing node held near 0 V by negative feedback.3) Because op-amp input current ~ 0, KCL forces the sum(Ik) to flow through the feedback element.4) The op-amp output supplies whatever current is required through the feedback to keep the summing node at virtual ground.

Verification / Alternative check:
Apply Kirchhoff’s current law at the summing node: sum(currents from sources) + input current + feedback current = 0. With input current ≈ 0, feedback current equals the negative sum of source currents, confirming the path is through feedback, not into the op-amp input pin.

Why Other Options Are Wrong:
“Correct” misunderstands op-amp input behavior. “Correct only for noninverting DACs” is irrelevant; the noninverting configuration still avoids input current. “Correct when the op-amp has finite input bias” confuses tiny bias currents with the large signal sum; bias is negligible compared to the functional current path.

Common Pitfalls:
Assuming current “flows into” an op-amp input; forgetting virtual ground; ignoring that the op-amp output stage delivers the necessary feedback current to satisfy KCL.

Final Answer:
Incorrect