In an R-2R ladder DAC, how do binary input bits map to output voltages and why is the ladder favored?

• A. Bits map to a continuous range via exponential weights; ladder uses a single resistor
• B. Bits control branches with weights that are powers of two; ladder uses only two resistor values, simplifying manufacturing
• C. Bits are encoded as frequency; ladder is faster
• D. Bits map to analog integrals; ladder minimizes noise

Answer: (B)

The key idea is that an R-2R ladder converts binary inputs into an analog voltage by steering a reference voltage through a network whose weights are powers of two. Each input bit controls a switch that either connects the corresponding node to Vref or to ground, and the repeating R and 2R structure ensures that each higher-order bit contributes exactly half as much as the one before it. As a result, the output is a weighted sum of the bits: Vout = Vref × (b1/2 + b2/4 + … + bN/2^N), where b1 is the most significant bit and bN the least significant. This binary-weighted output is what makes the DAC produce precise, monotonic steps as the digital input changes.

Why this ladder is favored: it uses only two resistor values, R and 2R, for every section, so matching and fabrication are much simpler, especially in integrated circuits. The uniform structure yields consistent ratios across the ladder, helping maintain accuracy and linearity, and it scales cleanly to more bits without introducing a variety of different parts. This combination of reliable weighting and manufacturing simplicity is what makes the R-2R ladder a preferred approach for DAC implementations.

This isn’t about continuous exponential weighting, frequency encoding, or integration; the ladder provides discrete, binary-weighted contributions that sum to the digital input in a straightforward, well-controlled way.