Neural network computing philosophy is proposed to model the major features of human brain and to apply neurons functionality to build Computers capable of simulating features of the brain. Memristor is a new device that stores data as memory element and perform logic operations as a computational element with low surface area and power consumption features. These characteristics of memristors have introduced them as a brilliant candidate for neural networks realization. In this paper, a threshold Integrate-and-Fire memristor based neuron is presented and is implemented by IMPLY logic with two 4-bits inputs, which is easily extendable to higher dimensions in terms of network scale and/or precision. Corresponding calculations are performed using adders and comparators, which requires 30 memristors in 131 computational steps.