We study the distributed average consensus problem in multiagent systems with directed communication links that are subject to quantized information flow. The goal of distributed average consensus is for the nodes, each associated with some initial value, to obtain the average (or some value close to the average) of these initial values. In this article, we present and analyze a novel distributed averaging algorithm that operates exclusively on quantized values (specifically, the information stored, processed, and exchanged between neighboring agents is subject to deterministic uniform quantization) and relies on event-driven updates (e.g., to reduce energy consumption, communication bandwidth, network congestion, and/or processor usage). We characterize the properties of the proposed distributed averaging protocol on quantized values and show that its execution, on any time-invariant and strongly connected digraph, will allow all agents to reach, in finite time, a common consensus value (represented as the ratio of two quantized values) that is equal to the exact average.