This invention addresses fixed-point representations of convolutional neural networks (CNN) in integrated circuits. When quantizing a CNN for a practical implementation there is a trade-off between the precision used for operations between coefficients and data and the accuracy of the system. A homogenous representation may not be sufficient to achieve the best level of performance at a reasonable cost in implementation complexity or power consumption. Parsimonious ways of representing data and coefficients are needed to improve power efficiency and throughput while maintaining accuracy of a CNN.