The leading zero anticipator (LZA) algorithm is very important for studying floating-point addition operation, and the analysis of floating-point addition indicates that the LZA  module plays a critical role in the performance improvement of  floating-point addition operations. We define a series of definitions and theorems from the perspective of prefix computation, and prove that the LZA algorithm can be attributed to a prefix computation problem in nature. Thus, the problem can be solved by the dichotomy recursive method. In LZA process, we firstly convert the prediction problem of two operations  to a digital string feature detection problem on numeric character set of {1,0, 1} by performing the subtraction of "Borrow Retirement" on addition operations. Secondly, a unified form of bit strings is obtained via the recoding technique which eliminates the continuous string of "1". Finally, the dichotomy recursive algorithm is designed based on the bit string structure of leading zero digits.