Parallel addition and subtraction in ternary mirror-symmetrical number system

Bergman has proposed an irrational number system where the golden ratio is used to be the base. The system has been improved by introducing a symmetrical concept to the representation, this new system is called ternary mirror-symmetrical number system. In this paper we are interested in parallel addition and subtraction problems. A modified version of on-the-fly architecture is applied to the system in order to perform addition and subtraction in parallel manner. Theoretical results show that addition and subtraction can be performed in Theta log(n) time complexity where n is the number of digits of the operands.