Instructions
Linear Feedback Shift Registers are very efficient and fast counters,
provided their non-binary count sequence is acceptable. The counter
consists of an n-bit shift register shifting left-to-right. The
rightmost bit and certain other bits are combined in an XNOR gate
and drive the D input of the leftmost bit.
The proper taps for dividing by 2n-1 are listed in the
app note : 
XAPP052: Efficient Shift Registers,
LFSR Counters and Long Pseudo-Random Sequence Generators.
It is easy to reverse the direction of such an LFSR counter:
- Reverse the direction of the shift register to right-to-left.
- Feed the D input of the right-most bit with the output of a
new XNOR gate.
The inputs to this new XNOR gate are similar to the XNOR gate for
the left-to-right case, but they are all rotated one position to
the right, and the leftmost bit takes the place of the rightmost
bit.
Use the example of a 15-bit up counter. If the bit positions are
counted as 1 through 15, left to right, then the XNOR of bits 14
and 15 feeds D input of position 1. The same counter running backwards,
shifting right-to-left: XNOR of positions 15 and 1 feeds D input
of position 15.
Advantages of LFSR counters: No carry logic, no carry delay, easy
to change direction, very easy to detect or decode previous or next
state.
Disadvantages of LFSR counters: Non-binary count sequence. The
sequence is one code short, and the counter would lock up if it
ever accidentally got into this illegal state (all Ones in the case
of the XNOR feedback). There are ways to avoid this problem, but
they involve additional logic and get rather complicated beyond
six bits.
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