Op Amp Digital to Analog Converter Circuit

Op Amp Digital to Analog Converter Circuit

This is a design circuit for a simple 4-bit digital-to-analog converter.  It is actually just a simple op amp summer circuit, i.e., an operational amplifier configured to output a voltage that is proportional to the sum of the input voltages. This is the figure of the circuit;

The op-amp summer circuit above works as a DAC because its input voltages are binary weighted with respect to each other, as set by the resistors (10K, 20K, 40K, 80K) at the inputs.  
 
The output Vo of this summer circuit w is:    
Vo = -VRef (5K) (S3/10K + S2/20K + S1/40K + S0/80K) = -VRef (S3/2 + S2/4 + S1/8 + S0/16) wherein S3, S2, S1, and S0 are the logic inputs ('1' or '0'). The number of bits of this DAC may be increased by connecting more switches with corresponding binary-weighted resistors to the inputs.