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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
V2 = Vin/4. This voltage drops across 2R to virtual common, so Iin = Vin/(4*2R) = Vin/(8R). So
Vout = -Vin/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.

S1 S2 S3 Vout
0 0 0  0
0 0 1  -Vin/8
0 1 0  
0 1 1  
1 0 0  
1 0 1  
1 1 0  
1 1 1  

Voila! Straight binary coding of the switches gives a voltage proportional to that binary number! In fact, if (in this example) Vin=-8 V, then Vout 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.



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