As deep neural networks (DNNs) advance, their computational demands have grown immensely.In this context, previous research introduced bit-wise computation to enhance silicon efficiency, along with skipping unnecessary zero-bit calculations.However, we observe that existing bit-wise approaches miss an opportunity to optimize the critical computation path, as they process groups of values sequentially from the most significant bits (MSBs) to the least significant bits (LSBs).To address this limitation, we propose BitL, a novel bit-wise computing unit designed to minimize the critical path and improve the throughput.BitL dynamically switches between horizontal and vertical data lookups across sub-tiles during Multiply-Accumulate (MAC) operations.Additionally, it presents an innovative optimization technique to maximize the utilization of computing units while switching its lookup direction.Our evaluation demonstrates that BitL delivers up to 1.92× higher throughput compared to a baseline DNN accelerator and achieves a 1.24× improvement over recent zero-bit skipping accelerators.Furthermore, BitL improves energy efficiency by 2.06× on average, with a silicon area overhead of only 5.71%.