This paper presents hardware-oriented symbolic execution that uses a recursive algorithm to find, and generate exploits for, vulnerabilities in hardware designs. We first define the problem and then develop and formalize our strategy. Our approach allows for a targeted search through a possibly infinite set of execution traces to find needle-in-a-haystack error states. We demonstrate the approach on the open-source OR1200 RISC processor. Using the presented method, we find, and generate exploits for, a control-flow bug, an instruction integrity bug and an exception related bug.