Compared to the most commonly used binary computers, the Fibonacci computer has its own research values. Making study of Fibonacci radix system is of considerable importance to the Fibonacci computer.

Most materials only explain how to use binary coefficients in Fibonacci base to represent positive integers and introduce a little about basic arithmetic on positive integers using complicated but incomplete methods. However, rarely have materials expanded the arithmetic to negative integers with an easier way.

In this thesis, we first transfer the unsigned binary Fibonacci representation with minimal form(UBFR(min)) into the even-subscripted signed ternary Fibonacci representation(STFRe), which includes the negative integers and doubles the range over UBFR(min). Then, we develop some basic operations on both positive and negative integers by applying various properties of the Fibonacci sequence into arithmetic. We can set the arithmetic range equivalent to 64-bit binary as our daily binary computers, or whatever reasonable ranges we want.