R–2R ladder DAC (4-bit) — how many distinct resistor values are required? A 4-bit R–2R ladder digital-to-analog converter is built using only replicated values. How many different resistor values are used in the ladder network?

Introduction / Context:
The R–2R ladder is a highly practical DAC topology because it uses only two resistor values, regardless of resolution. This greatly simplifies matching and scaling compared with binary-weighted DACs that require precise powers-of-two resistor ratios. Understanding this property explains why R–2R ladders are common in integrated DACs and lab circuits alike.

Given Data / Assumptions:

• We consider a standard R–2R ladder DAC for 4 bits.
• Ideal resistors are perfectly matched.
• Switches connect each bit node either to reference or ground.

Concept / Approach:
In an R–2R ladder, the entire network is formed by repeating segments that contain only R and 2R. Each bit adds another rung of the ladder with the same two values, ensuring that the Thevenin equivalent seen by each bit is properly scaled. The number of bits changes the number of components but never the number of distinct values required.

Step-by-Step Solution:

Verification / Alternative check:
Textbook schematics confirm that any N-bit R–2R DAC repeats the same two values. SPICE simulations with R = 10 kΩ and 2R = 20 kΩ demonstrate the expected binary-weighted outputs for all 4-bit codes.

Why Other Options Are Wrong:

• One value: impossible, as the ladder requires both R and 2R.
• Three/four values: unnecessary—would defeat the ladder’s simplicity.
• “Depends on bits”: incorrect; the beauty of the ladder is independence from N.

Common Pitfalls:

• Confusing R–2R with binary-weighted DACs that need R, 2R, 4R, 8R, etc.

Final Answer:
two resistor values