Free-space optical interconnections are important both in massive digital optical computing and in communication systems.The optical butterfly interconnection has many advantages over other intercon-nections in implementing various basic logic functions such as addition

subtraction

multiplication.This paper starts with the convent-ional Karnaugh maps and Boolean algebra to implement a parallel n-bit ripple carry full adder by the use of multilayer butterfly interconnection networks.Then we describe in detail the design and architecture of the full adder and provide accurate interconnection networks and the structures or patterns of key devices such as the masks to implement AND and OR operations in this calculation. Finally

we discuss development of the interconnection in implementing logic operations.