High speed and power are required for modern applications, and low power consumption and a small integration area. So, this system will be consumed less power. To manipulate these problems either way of computing should be changed by another technique or the transistor should be changed by another device. One selective computing is stochastic. While loaded computing contributes high hardware cost, high speed. Stochastic computing accuracy is less than binary computing circuits. They are having some implementation basic operations of stochastic computing. They are complementary operation, multiplication operation, addition operation, subtraction operation, and division operation. These operations having some logic gates i.e., AND gate, NOT gate, XOR gate, an XNOR gate. And implement the hardware Tripartite synapse. It can be divided into parts. They are Astrocyte, Synapse, Input spiking, LIF neuron, and output spiking. Using stochastic circuits and conversion processes, this paper demonstrates the fundamental notions of stochastic computing. implementation of arithmetic operations and hardware tripartite synapse and tripartite synapse hardware architecture.