a binary-weighted DAC

The binary-weighted DAC is the most direct way to turn a number into a voltage: give every bit its own switch and its own resistor, and make each bit contribute exactly its place value. It is like making change with coins where each coin is worth twice the last — a 1, a 2, a 4, an 8 — and you simply decide for each coin whether to drop it in. Add up the coins you chose and you have the number, now as a current or voltage.

Mechanically, each bit drives a resistor connected to the reference, and the resistor values follow the binary weights: R, then 2R, then 4R, then 8R, and so on, halving the current each step down. The most significant bit, with the smallest resistor R, pushes the biggest current; the least significant bit, with the largest resistor, pushes the smallest. A summing op-amp adds all the switched-in currents into one output voltage. Turn on the bits set to 1, and their currents add to exactly the right total — bit 3 contributes 8 units, bit 2 contributes 4, and so on.

Why this matters, and why it is rarely used at high resolution: the idea is beautifully simple but the resistor values span an enormous range. For 8 bits the largest resistor is 128 times the smallest; for 16 bits it is over 65,000 times. Making a 1 kohm and a 65 Mohm resistor match to better than one part in 65,000, and track each other over temperature, is wildly impractical. That is the whole reason the R-2R ladder was invented — it gets the same binary weighting using only two resistor values, dodging this impossible spread.