A novel method of digit shifting in a bidirectional shift register is described which provides substantial saving of components in terms of gates. In this method only the bits occupying the 1-position of the 8-4-2-1 code can shift in either direction. Bits of the same digit position are then made to change place among themselves. Eight clock pulses are required to shift the bits through one digit position, but the number of clock pulse requirement is independent of the number of digits involved in the shifting process. However, this shortcoming of speed reduction can be overcome by providing a separate clock for this purpose which may be several times faster than the system clock. The drastic reduction in component count and cost of the new method over the conventional one has also been illustrated. These together with the reduction of interconnecting leads and power dissipation leads to the possibility of fabricating multidigit bidirectional shift registers in monolithic integrated circuit packages.