The verification of hardware design code is a critical aspect in ensuring the quality and reliability of hardware products. Finding bugs in hardware design code is important for hardware development and is frequently considered as a notoriously challenging and time-consuming activity while being an essential aspect of verification. Thus, bug localization techniques that could assist manual debugging have attracted much attention in the hardware community. However, there exists an unpredictable time span between the precise origin of a bug and its detected manifestation in prior work without costly formal verification. Locating the bug responsible for the exposed discrepancy between expected and exhibited design behavior remains a major challenge. In this work, we propose Tartan, a
T
ime-
a
ware spect
r
um-based bug localiza
t
ion with d
a
ta purificatio
n
for hardware design code to address these limitations. Tartan integrates hardware-specific timing information with the spectrum and captures the changes of executed statements when the state of the circuit changes to effectively locate bugs. Further, Tartan purifies the spectrum data from the simulation and evaluates the suspiciousness of the statements in the design to indicate the likehood of being buggy. To evaluate the effectiveness of Tartan, we conduct large-scale experiments on 69 versions of 15 hardware projects by the state-of-the-art bug localization techniques. The experimental results clearly show that Tartan is statistically more effective than the baselines. It provides a new perspective on hardware design code bug localization and brings fresh insights to the community.