  Using the classic two's complement notation of signed integers, the
fundamental arithmetic operations of addition, subtraction, and multiplication
are identical to those for unsigned binary numbers. We introduce a
Fibonacci-equivalent of the two's complement notation and we show that addition
in this numeration system can be performed by a deterministic finite-state
transducer. The result is based on the Berstel adder, which performs addition
of the usual Fibonacci representations of nonnegative integers and for which we
provide a new constructive proof. Moreover, we characterize the
Fibonacci-equivalent of the two's complement notation as an increasing
bijection between $\mathbb{Z}$ and a particular language.
