In this paper, we implemented sigmoid active function which make it difficult to design of the digital neuron networks. Therefore, we designed of the high speed processing of the sigmoid function in order to digital neural networks. we designed of the MAC(Multiplier and Accumulator) operation unit used residue number system without carry propagation for the high speed operation. we designed of MAC operation unit and sigmoid processing unit are proved that it could run of the high speed. On the simulation, the faster than 4.6ns on the each order, we expected that it adapted to the implementation of the high speed digital neural network.