The general DSP algorithm, like orthogonal transform or filter processing, needs efficient hardware architecture to compute inner product. The typical MAC architecture has high cost of silicon. Because of this reason, the distributed arithmetic without multiplier is widely used for implementing inner product. This paper presents the optimization to reduce required hardware in distributed arithmetic by using extraction method of adder sharing component. The optimization process uses Boltzmann-machine which is one of the neural network. This proposed method can solve problem that is increasing complexity depending on depth of inner product and compose optimal summation-network with the minimum FA and FF in a few time. The designed DCT by using Proposed method is more efficient than a ROM-based distributed arithmetic.