Bubble Pushing Shift Register

This will be just and quick post, and IT HAS PICTURES!!!  I am working on a bi-directional shift register for tracking and moving the car and I thought I would share a simple technique for reducing gate counts or in my case keeping everything NAND.  It is called bubble pushing.  Check out this PDF from Oklahoma State University on the subject, pages 14-18.

This is a key component of the bi-directional shift register. It can be simplified by bubble pushing.

Both the top and bottom block function as an OR gate.

Replace the OR gate with the three NAND gates.

The Double NOR (NAND) gates cancel giving the final result.  This also converts it to an all NAND gate configuration as well as reducing the gate count by 2 per output.