Linear binary shift register circuits utilizing a minimum number of mod-2 adders

Author

Roth, Herbert H.

Volume

Issue

fYear

1965

fDate

4/1/1965 12:00:00 AM

Firstpage

215

Lastpage

220

Abstract

A family of linear binary shift register circuits is described in terms of generator polynomials $g(x)$ which require fewer mod- $2$ adders than those derived from the companion matrices. These circuits are derived from various combinations of the functions $a(x), b(x)$ , and $x^{d}$ in $g(x) = 1 + a(x)x^{d}b(x)$ and $c(D), e(D)$ , and $D^{m}$ of the reciprocal polynomial $g^{\\ast }(x) = f(D) = 1 + c(D)D^{m}e(D)$ . Tables are provided for all simplifications thus achievable for primitive polynomial of degrees $5$ through $9$ , and for some nonprimitive polynomials.

Keywords

Coding; Shift registers; Adders; Delay; Feedback circuits; Feedback loop; Flip-flops; Gyroscopes; Integrated circuit interconnections; Neck; Polynomials; Shift registers;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.1965.1053747

Filename

1053747

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=906143