A new class of shift registers that shift the contents of a 2.sup.n bit length register up to 2.sup.n -1 positions in n cycles. Shift registers according to the present invention can be constructed to shift left, shift right, or to shift either left or right. A general implementation of this class of shift registers comprises the following hardware: 2.sup.n D flip-flops or D latches for the data register positions of the shift register; logic for each of the 2.sup.n positions to determine the input value to which the position should take on at each of the n cycles; an n bit shift count register to store a value indicating the number of positions to shift; control lines specifying whether to shift left or right; n control lines which are sequentially raised for one cycle to select a bit in the shift count register for the current cycle beginning with the most significant bit and continuing sequentially to the least significant bit; and a clock to set the selected input data to each position in the shift register.
