If all of the switches are to the left, no current comes to the inverting input of the amplifier, and output = 0 V. What if only S3 is to the right? We already know that

V_{2} = V_{in}/4. This voltage drops across 2R to virtual common, so I_{in} = V_{in}/(4*2R) = V_{in}/(8R). So

V_{out} = -V_{in}/8. Now fill in the following table. A "0" for a switch means it is connected to physical ground, while a "1" means it is connected to virtual common on the amplifier. Clicking anywhere in the table to pop up a window showing the full set of values.

Voila! Straight binary coding of the switches gives a voltage proportional to that binary number! In fact, if (in this example) V_{in}=-8 V, then V_{out} is the binary number, expressed in volts.

It is now clear how a straight binary DAC works -- one simply uses an R/2R network and an appropriate reference potential.