Collatz conjecture (or 3x+1 problem) has not been proved to be true or false for about 80 years. The exploration on this problem seems to ask for introducing a totally new method. In this paper, a mathematical induction method is proposed, whose proof can lead to the proof of the conjecture. According to the induction, a new representation (for dynamics) called ``code'' is introduced, to represent the occurred $3*x+1$ and $x/2$ computations during the process from starting number to the first transformed number that is less than the starting number. In a code $3*x+1$ is represented by 1 and $x/2$ is represented by 0. We find that code is a building block of the original dynamics from starting number to 1, and thus is more primitive for modeling quantitative properties. Some properties only exist in dynamics represented by code, but not in original dynamics. We discover and prove some inherent laws of code formally. Code as a whole is prefix-free, and has a unified form. Every code can be divided into code segments and each segment has a form $\{10\}^{p \geq 0}0^{q \geq 1}$. Besides, $p$ can be computed by judging whether $x \in[0]_2$, $x\in[1]_4$, or computed by $t=(x-3)/4$, without any concrete computation of $3*x+1$ or $x/2$. Especially, starting numbers in certain residue class have the same code, and their code has a short length. That is, $CODE(x \in [1]_4)=100,$ $CODE((x-3)/4 \in [0]_4)=101000,$ $CODE((x-3)/4 \in [2]_8)=10100100,$ $CODE((x-3)/4 \in [5]_8)=10101000,$ $CODE((x-3)/4 \in [1]_{32})=10101001000,$ $CODE((x-3)/4\in [3]_{32})=10101010000,$ $CODE((x-3)/4\in [14]_{32})=10100101000.$ The experiment results again confirm above discoveries. We also give a conjecture on $x \in [3]_4$ and an approach to the proof of Collatz conjecture. Those discoveries support the proposed induction and are helpful to the final proof of Collatz conjecture.