An important issue in analog circuit design is the problem of digital-to-analog conversion, i.e., the encoding of Boolean variables into a single analog value which contains enough information to reconstruct the values of the Boolean variables. A natural question is: What is the complexity of implementing the digital-to-analog encoding function? That question was recently answered by Wegener, who proved matching lower and upper bounds on the size of the circuit for the encoding function. In

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... icular, it was proven that d(3n 0 1)=2e 2-input arithmetic gates are necessary and sufficient for implementing the encoding function of n Boolean variables. However, the proof of the upper bound is not constructive. In this paper, we present an explicit construction of a digitalto-analog encoder that is optimal in the number of 2-input arithmetic gates. In addition, we present an efficient analog-todigital decoding algorithm. Namely, given the encoded analog value, our decoding algorithm reconstructs the original Boolean values. Our construction is suboptimal in that it uses constants of maximum size n log n bits; the nonconstructive proof uses constants of maximum size 2n + dlog ne bits.