We investigate the problem of feedback stabilization of networked control linear systems with unknown initial state. In particular, the sampling and the quantization effects of network are considered and we propose a quantized event-triggered control technique to handle this case. To cope with unknown initial state, a novel exponential dynamic quantizer is synthesized, which enables to capture the state in a finite time. Moreover, the dynamic quantization policy only depends on the sign of the quantization error and allows for one-bit transmission rather than packet-based transmission, which is desirable in practice. Then, the quantized state measurements are transmitted to the controller using an event-triggering mechanism to reduce the amount of transmissions over the network. The approach ensures global asymptotic stability property for the closed-loop system and prevents the occurrence of Zeno behavior. The entire closed-loop system is represented as a hybrid dynamical system and the closed-loop stability is assessed using suitable Lyapunov functions. The effectiveness of the proposed approach is demonstrated through numerical simulations.