With the two's complement notation of signed integers, the fundamental arithmetic operations of addition, subtraction, and multiplication are identical to those for unsigned binary numbers. In this work, we consider a Fibonacci-equivalent of the two's complement notation. A theorem of Zeckendorf says that every nonnegative integer can be represented as the sum of distinct nonconsecutive Fibonacci numbers thus leading to a binary representation of nonnegative integers where powers of 2 are replaced by Fibonacci numbers in its evaluation. A transducer provided by Berstel computes the sum of the Zeckendorf binary representation of two nonnegative integers. In this work, we consider a numeration system also based on Fibonacci numbers but representing all integers. As for the two's complement notation, we show that addition of integers represented in this numeration system can be computed with the Berstel transducer with three additional transitions. Whether this can be done more generally is an open question raised by the current work.