I am a new learner of optimization, and I am confused by the question below, (how to change a 0-norm constrain into binary and linear constrain ?)

Given a sparse data fitting problem:

$ minimize \quad \| Ax-b \|^{2}_{2}$

$ s.t. \qquad \|x\|_{0} \le K, $

$x \in R^{n}$

Suppose we are given a constant $M > 0$ such that $\|x^{*}\|_{\infty} \le M$ for some optimal solution $x^{*}$ to this problem. How can we paraphrase this problem with only linear and binary constraints?

Thanks for any help.