Discuss the significance of Gray code in digital systems, particularly in minimizing errors in analog-to-digital conversions and other applications.

Gray code is a binary numeral system where two successive values differ in only one bit, reducing the likelihood of errors during transitions. This property is vital in analog-to-digital conversion, where minor errors can cause significant inaccuracies. Gray code helps ensure accurate digital representation of analog signals and is used in rotary encoders and error correction in digital communication systems.