Generalized Single-Ended Counters

ABSTRACT

Conventional shift counters are shown to be a special case of the general class of counters that use single-ended information on all but one bit position of JK flip-flops. The resultant class of counters preserves the autocorrelation characteristics necessary for pseudo-random number generation while allowing a saving in the physical mechanization of a given characteristic equation. A companion matrix in canonical form is developed that yields a direct mapping from the characteristic equation to the requisite logic on each flip-flop.

REFERENCES

• 1: John S. Bailey , George Epstein, Single Function Shifting Counters, Journal of the ACM (JACM), v.9 n.3, p.375-378, July 1962 [doi>10.1145/321127.321134]
• 2: ELSPAS, B. Tile theory of autonomous linear sequential networks. IRE Trans. on Circuit Theory 6 (Mar. 1959), 45-60.
• 3: G. B. Fitzpatrick, Synthesis of Binary Ring Counters of Given Periods, Journal of the ACM (JACM), v.7 n.3, p.287-297, July 1960 [doi>10.1145/321033.321042]
• 4: MAasu, R. W. Table of irreducible polynomials over GF (2) through degree 19. U.S Dept. of. Commerce, Oct. 24, 1957.
• 5: PETERSON, W.W. Error Correcting Codes. MIT Press, Cambridge, Mass., I961.
• 6: Frederick H. Young, Analysis of Shift Register Counters, Journal of the ACM (JACM), v.5 n.4, p.385-388, Oct. 1958 [doi>10.1145/320941.320953]

INDEX TERMS

Primary Classification:
  B. Hardware
  B.5 REGISTER-TRANSFER-LEVEL IMPLEMENTATION

Additional Classification:
  G. Mathematics of Computing
  G.2 DISCRETE MATHEMATICS

General Terms:
Measurement, Performance, Theory