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This paper considers implementation of artificial neural networks (ANNs) using molecular computing and DNA based on fractional coding. Prior work had addressed molecular two-layer ANNs with binary inputs and arbitrary weights. In prior work using fractional coding, a simple molecular perceptron that computes sigmoid of scaled weighted sum of the inputs was presented where the inputs and the weights lie between [-1,1]. Even for computing the perceptron, the prior approach suffers from two major limitations. First, it cannot compute the s