Turing Compute Model for Non-negative Binary Numbers

Abstract

Turing-computable issue is important in research of Turing Machine and has significant value in both theory and practice. The paper analyzes Turing-computable issue of non-negative numbers by relational operations(includes greater than, less than and equal) and arithmetic operations(includes add operation, subtract, multiply, divide and modulo). The regulation of computing 1-bit binary number and the carry set(or borrow set) are defined to compute multi-bit binary numbers. Algorithms are described through multi-tape Turing machine. For some operations, the discussion is extended to base-N number system(3≤N≤10). Turing regulation for add operation is used to implement the Turing counter for counting the length of the string on the input tape of the Turing machine.