LFSR Tools and Feedback Taps

Written by Jay Dowling September 25, 2009 Hits: 1235 Favorites

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Thanks to Max for sharing his series of articles (Part 1, Part 2, Part 3) that serve as an introduction to LFSR’s, all excerpts from Appendix E of his wonderful book Bebop to the Boolean Boogie: An Unconventional Guide to Electronics (my review).

For now I’ll assume you’ve read the above explanations from Max or you’re already familiar with the intricacies of LFSRs. So let’s put the petal to the metal and give you some information that you can apply to your designs.

Jean Nicolle has a wonderful freeware tool for selecting and generating LFSRs. With it, you can generate a table of output values and source code in Verilog, VHDL or AHDL for your desired LFSR module. First you select the number of states in the sequence or the number of bits in the shift register. In the latter case, you can input the feedback taps manually or have them automatically selected. Then you can select a one-to-many or many-to-one feedback structure as well as XOR or XNOR feedback gates. Additionally, for those cases where 2ⁿ-1 maximal states are insufficient you can even select 2ⁿ states as an option. It even draws a nice schematic of your completed LFSR. You can download the program from here or from his webpage where there are some other items that may be bare investigation.

Those of you just looking for feedback taps might want to check out some of the following references. For register widths of 4 to 39 bits, Philip Koopman has created individual text files containing feedback taps available for download here. At the end of Xilinx application note XAPP052 is a table of feedback taps ranging from 3 to 168 bits. More demanding readers may want register widths in the range of 2 to 786 or perhaps even 1024, 2048 or 4096 bits that Roy Ward and Tim Molteno have made available here.

In the future we’ll cover some finer nuances of LFSRs, some of their mathematical basis, other feedback taps of the same degree as those provided above and how the math is shared with other interesting things besides LFSRs.

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Written by :

Jay Dowling