# Digital-to-analog conversion of a product of digital inputs

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

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 $7.5R_0$.