A shift register, generally consisting of a number of cells, several parallel outputs of which are combined in a combinational logic function. An important case is the linear feed-forward register in which linear logic is employed for the feed-forward function.

The linear feed-forward register has the effect of convolving the serial input to the register with the sequence of combinational coefficients (see convolution). If the input is regarded as a polynomial in which powers of the indeterminate denote succession in time, and if the combinational coefficients are regarded likewise as a second polynomial, then the linear feed-forward register has the effect of multiplying these polynomials.

When used in coding or in digital signal processing, feed-forward registers may be binary or q-ary, and may be implemented in hardware or software.