Automated design methods for convolutional neural networks (CNNs) have recently been developed in order to increase the design productivity. We propose a neuroevolution method capable of evolving and optimizing CNNs with respect to the classification error and CNN complexity (expressed as the number of tunable CNN parameters), in which the inference phase can partly be executed using fixed point operations to further reduce power consumption. Experimental results are obtained with TinyDNN framework and presented using two common image classification benchmark problems -- MNIST and CIFAR-10.