Latest developments in the field of power-efficient neural interface circuits provide an excellent platform for applications where power consumption is the primary concern. Developing neural networks to achieve pattern recognition on such hardware remains a daunting task owing to substantial computational complexity. We propose and demonstrate a Spiking Neural Network (SNN) with biologically reasonable time constants to implement basic Boolean Logic Gates. The same network can be further applied to more complex problem statements. We employ a frequency spike encoding for data representation in the model, and a simplified and computationally efficient model of a neuron with exponential synapses and Spike Timing Dependent Plasticity (STDP).