One of the key elements in an artificial neural networks (ANNs) is the activation function (AF), that converts the weighted sum of a neuron's input into a probability of firing rate. The hardware implementation of the AF requires complicated circuits and involves a considerable amount of power dissipation. This renders the integration of a number of neurons onto a single chip difficult. This paper presents circuit techniques for realizing four different types of AFs, such as the step, identity, rectified-linear unit (ReLU), and the sigmoid, based on stochastic computing. The proposed AF circuits are simpler and consume considerably lesser power than the existing ones. A handwritten digit recognition system employing the AF circuits has been simulated for verifying the effectiveness of the techniques.