:PROPERTIES: :ID: 86d6f108-b55c-4def-8748-c0f22c0b2854 :mtime: 20231011034037 :ctime: 20231011033926 :END: #+title: Fast Carry Generation #+filetags: :public:project: * Definition Fast Carry Generation (FCG) is a method for speeding up the addition of binary numbers. FCG is faster than [[id:659ca8e1-12cc-4fde-81ab-a9abad3aa5bb][Ripple Carry Adder]]. The way it works is that it generates the carry bits in parallel. * How FCG Works ** Carry Kill $k_i = \overline{a_{i}}.\overline{b_{i}}$ ** Carry Propagate $p_{i} = a_{i} \oplus b_{i}$ ** Carry Generate $g_{i} = a_{i}.b_{i}$ ** Carry Generation $c_{i+1} = g_{i} + c_{i}.p_{i}$ And $c_4 = G + c_{0}.P$