The Use of Circuit Codes in Analog-To-Digital Conversion

摘要

A d-dimensional Gray code (or, equivalently, a d-dimensional circuit code of spread 1 and length 2 to the d) is a Hamiltonian circuit in the graph I(d) of a d-dimensional cube. Such codes are commonly used to minimize the inevitable quantization error in the analog-to-digital conversion of serial data, and they are also used in the design of counters for purely digital systems. By using circuit codes of spread greater than 1, additional error-checking features can be introduced. A basic and difficult problem has been that of determining, for each d and s, the maximum length of d-dimensional circuit codes of spread s. The report contains an exposition of the known partial results on that problem, along with some suggestions for further research. (Author)