Abstract: 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.