Decomposition of linear sequential circuits over residue class rings

✍ Scribed by Mario Magidin Matluk; Arthur Gill

• Publisher: Elsevier Science
• Year: 1972
• Tongue: English
• Weight: 694 KB
• Volume: 294
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(72)90012-9

✦ Synopsis

In this paper we show that every linear sequential circuit (LSC) dejined over a residue class ring Z,, where m = po;' pp . . . p;k (the pi being distinct primes), is isomorphic to a parallel connection of k LSC's over Z,lri (i = 1, 2, . . . . k); each LSC over Z,,rg is, in turn, isomorphic to a cascade connection of ri LSC's over Z,, (that is, over the Galois field GF(pJ ), where the cascaded stages are separated by a (generally nonlinear) delay-free logic. Thus, every LSC over a residue class r&g is isomorphic to an interconnection of LSC's over Galois Jields.