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If we have a 4-bit DAC, which converts a 4-bit binary signal \$ X = X_3 X_2 X_1 X_0\$ to an analog signal \$Y=X/2\$ (i.e. 1010 -> = 5 V, or 0111 -> 3.5 V).

How can we create a DAC, using any number of upper-mentioned DACs, OpAmps, and lower level circuits (Like And, Or, Xor, etc) that converts the number: \$ \displaystyle\frac{X\cdot Y}{4} \$ to analog value (i.e. X = 1010, Y = 0011 -> 10*3/4 = 7.5 V)

THanks

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The best option is to multiply digital inputs and feed them to an 8-bit DAC. But if you have some spare 4-bit DACs, Opamps and resistors, it's possible to do a different way.

  1. Feed the first digital input to the first DAC, use some constant voltage source as the reference voltage
  2. Feed the second digital input to the second DAC and use the first DAC's output as its reference. If the DAC requires both positive and negative reference, use an opamp to invert the first DAC's output and feed the opamp's output to the negative reference input of the second DAC.
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  • \$\begingroup\$ Great idea, thanks! However, I calculated my DAC "transfer" function as: V_out = -X/40 * V_ref. So if I do as you suggested, I get: V_out = X*Y/1600 * V_ref. If I wanted my XY/4 value, I would need a 400V reference voltage, right? :P \$\endgroup\$ – Vidak Feb 7 '14 at 3:00
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Take four DACs, \$D_0,\ D_1,\ D_2, D_3\$, and for DAC \$D_i\$ use \$(X\$ and \$Y_i)\$ as the input (or gate the DAC in some other way using \$Y_i\$). Take the outputs of the DAC into a voltage summing OpAmp using binary weighted resistances, \$R_i\$, connecting each output to the input of the OpAmp. \$R_i = 2R_{i+1}\$ and the feedback resistance being \$7.5R_0\$.

The main challenge would be to get more than 60 V out of the OpAmp, so make sure you buy ones that could handle it (or whatever maximum voltage you prefer, change the feedback resistance accordingly).

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