Binary-weighted DAC resistor values Assess the statement: “In a binary-weighted digital-to-analog converter (DAC), the input resistors are chosen proportional to the binary weights of the corresponding input bits.” Select the best assessment.

Introduction / Context:Two common DAC topologies are binary-weighted resistor DACs and R–2R ladder DACs. In a binary-weighted DAC, each input bit contributes an analog current or voltage weighted in proportion to its binary significance (MSB contributes twice that of the next, and so on). The resistor network must therefore be sized to implement these binary weights.

Given Data / Assumptions:

• The DAC is specifically of the binary-weighted type, not an R–2R ladder.
• Each bit drives a switch connected through a resistor to a summing node (current or voltage summing).
• Reference source is constant; linear operation is assumed.

Concept / Approach:For binary weighting, the contribution of bit k is proportional to 2^k relative to the LSB. Using resistors, this is achieved by setting their values inversely proportional to the desired current: I = V / R. Thus, to double the weight, halve the resistance. Typical networks choose R, R/2, R/4, ... for MSB→LSB (or the reciprocal, depending on orientation). This directly encodes the binary weights into the resistor values.

Step-by-Step Solution:

Verification / Alternative check:Contrast with R–2R: that topology uses only two resistor values (R and 2R), avoiding wide tolerance spread; binary-weighted explicitly scales resistors by powers of two.

Why Other Options Are Wrong:

Common Pitfalls:Assuming R–2R behavior applies to binary-weighted DACs; mixing up voltage-mode and current-mode implementations.

Final Answer:Correct