New low power adders based on new representations of carry signals

The carry signals are crucial in binary addition of two numbers. There are many kinds of carries including the traditional carry, Ling's carry, and the carry for adders based on redundant arithmetic. The traditional carry is conventionally generated by the "recursive doubling" method or the "fco" operator. This paper first proposes a uniform representation of various carry signals using function graphs, which are more powerful than both "recursive doubling" and "fco" operator. Based on the function graphs of carries, we present new adder implementations using MUXes. The new adders can save from 50% to 15% fewer MUXes for different adders. We further demonstrate that contrary to a previous result, Ling's carry can be efficiently implemented using MUX with a slight speed advantage.