1. A digital signal processor dedicated to digital signal processing, comprising a memory portion, a control portion, an arithmetic operation portion and a data bus serving as a data transmission line among said memory portion, said control portion and said arithmetic operation portion, said memory portion comprising: first storing means for storing part of first data to be multiplied, and second storing means for storing second data to be multiplied with said first data, at least one of said first and second storing means being formed by shift register means comprising pluralities of sequentially addressable memory cells, each for storing a fixed length memory data word, address input means for receiving a data word address signal and in response to uniquely decode said address signal for enabling a corresponding one of said pluralities of memory cells containing a particular data word, data input means for storing data in a first one of said pluralities of memory cells, data output means for outputting data from any one of a plurality of memory cells designated by said address input means to said data bus and to a multiplier, and data shifting means of shifting data into said first memory cell and for shifting data out of said first memory cell and through said pluralities of memory cells, said control portion comprising: a program memory for storing data, reading means for reading out successively said program data stored in said program memory, and means for providing to said memory, control and arithmetic operation portions respective control signals based on said program data read out from said program memory, and further including means for supplying a data word address signal to said address input means of said memory portion, said arithmetic operation portion comprising: said multiplier connected directly with said first and second storing means for multiplying data provided from said first storing means by data provided from said second storing means, an arithmetic logic unit connected directly with said multiplier, and an accumulator for storing temporarily an output of said arithmetic and logic unit, so that said output is supplied to said data bus.