Editing Linear-feedback shift register (section)

=== Uses as counters ===
The repeating sequence of states of an LFSR allows it to be used as a [[clock divider]] or as a counter when a non-binary sequence is acceptable, as is often the case where computer index or framing locations need to be machine-readable.<ref name="xilinx.com"/> LFSR [[Counter (digital)|counter]]s have simpler feedback logic than natural binary counters or [[Gray-code counter]]s, and therefore can operate at higher clock rates. However, it is necessary to ensure that the LFSR never enters a lockup state (all zeros for a XOR based LFSR, and all ones for a XNOR based LFSR), for example by presetting it at start-up to any other state in the sequence. It is possible to count up and down with a LFSR. LFSR have also been used as a [https://github.com/howerj/lfsr-vhdl Program Counter for CPUs], this requires that the program itself is "scrambled" and it done to save on gates when they are a premium (using fewer gates than an adder) and for speed (as a LFSR does not require a long carry chain).

The table of primitive polynomials shows how LFSRs can be arranged in Fibonacci or Galois form to give maximal periods. One can obtain any other period by adding to an LFSR that has a longer period some logic that shortens the sequence by skipping some states.