This work presents the design and analysis of a mixed-signal neuron (MS-N) for convolutional neural networks (CNN) and compares its performance with a digital neuron (Dig-N) in terms of operating frequency, power and noise. The circuit-level implementation of the MS-N in 65 nm CMOS technology exhibits 2-3 orders of magnitude better energy-efficiency over Dig-N for neuromorphic computing applications - especially at low frequencies due to the high leakage currents from many transistors in Dig-N. The inherent error-resiliency of CNN is exploited to handle the thermal and flicker noise of MS-N. A system-level analysis using a cohesive circuit-algorithmic framework on MNIST and CIFAR-10 datasets demonstrate an increase of 3% in worst-case classification error for MNIST when the integrated noise power in the bandwidth is ~ 1 {mu}V2.