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Using the classic two's complement notation of signed integers, thefundamental arithmetic operations of addition, subtraction, and multiplicationare identical to those for unsigned binary numbers. We introduce aFibonacci-equivalent of the two's complement notation and we show that additionin this numeration system can be performed by a deterministic finite-statetransducer. The result is based on the Berstel adder, which performs additionof the usual Fibonacci representations of nonnegative integers and for which weprovide a new constructive proof. Moreover, we characterize theFibonacci-equivalent of the two's complement notation as an increasingbijection between $\mathbb{Z}$ and a particular language.

A Fibonacci analogue of the two's complement numeration system