Title :
A smooth dynamical system that counts in binary
Author :
Greenstreet, Murk R. ; Xuemei Huang
Author_Institution :
Dept. of Comput. Sci., British Columbia Univ., Vancouver, BC, Canada
Abstract :
This paper presents a smooth dynamical system that implements a toggle flip-flop. The flip-flop is described as a system of smooth, non-linear ODEs. We identify a period-2, invariant set of this system, and show that this corresponds to the discrete state transitions of a discrete model. We show that this behaviour is robust for a large class of inputs and that these toggle elements can be composed to implement a binary counter of any number of bits
Keywords :
counting circuits; flip-flops; nonlinear differential equations; phase space methods; binary counter; discrete state transitions; nonlinear ODEs; period-2 invariant set; toggle elements; toggle flip-flop; Computer science; Counting circuits; Differential equations; Fabrication; Flip-flops; Mathematical model; Nonlinear equations; Robustness; SPICE; Semiconductor device modeling;
Conference_Titel :
Circuits and Systems, 1997. ISCAS '97., Proceedings of 1997 IEEE International Symposium on
Print_ISBN :
0-7803-3583-X
DOI :
10.1109/ISCAS.1997.621883
