Two novel full adder architectures are proposed that can be implemented with optical couplers using fiber optics or integrated optics. The first adder has the advantage over other proposed approaches by requiring only three different component devices: optical logical OR, optical logical NOT, and optical couplers. Configurations of the three components are described that are relatively simple to implement and are expected to function at greater than gigabit per second rates. The second adder requires fewer gates by using additional different gates: analog ADD and thresholding. Methods of implementing in fiber optics and with integrated optics are suggested including the synchronization of the lasers and methods for changing phase. The optical full adder can be used to provide high speed word addition by multiplexing independent additions. The pros and cons of fiber optics versus integrated optics for one architecture versus the other are discussed.