Optical computing has shown immense application prospects in the post-Moore era. However, as a crucial component of logic computing, the digital multiplier can only be realized on a small scale in optics, restrained by the limited functionalities and inevitable loss of optical nonlinearity. In this paper, we propose a time-space multiplexed architecture to realize large-scale photonic-electronic digital multiplication. We experimentally demonstrate an 8×2-bit photonic-electronic digital multiplier, and the multiplication with a 32-bit number is further executed at 25 Mbit/s to demonstrate its extensibility and functionality. Moreover, the proposed architecture has the potential for on-chip implementation, and a feasible integration scheme is provided. We believe the time-space multiplexed photonic-electronic digital multiplier will open up a promising avenue for large-scale photonic digital computing.