Interferometric devices have drawn great interest in all-optical signal processing for their high-speed photonic activity. Quantum-dot semiconductor optical amplifier (QD-SOA)-based gate has added a new momentum in this field to perform all-optical logic and algebraic operations. In this paper, for the first time, a new scheme for all-optical full adder using fife QD-SOA based Mach-Zehnder interferometers is theoretically investigated and demonstrated. The proposed scheme is driven by three input data streams; two operands and a bit carried in from the next less significant stage. The proposed scheme consists of two XOR, two AND, and one OR gate. The impact of the peak data power as well as of the QD-SOAs current density, maximum modal gain, and QD-SOAs length on the ER and Q-factor of the switching outcome are explored and assessed by means of numerical simulation. The operation of the system is demonstrated with 160 Gbit/s.