In recent years, there has been a significant push to implement Deep Neural Networks (DNNs) on edge devices, which requires power and hardware efficient circuits to carry out the intensive matrix-vector multiplication (MVM) operations. This work presents hardware efficient MVM implementation techniques using bit-serial arithmetic and a novel MSB first computation circuit. The proposed designs take advantage of the pre-trained network weight parameters, which are already known in the design stage. Thus, the partial computation results can be pre-computed and stored into look-up tables. Then the MVM results can be computed in a bit-serial manner without using multipliers. The proposed novel circuit implementation for convolution filters and rectified linear activation function used in deep neural networks conducts computation in an MSB-first bit-serial manner. It can predict earlier if the outcomes of filter computations will be negative and subsequently terminate the remaining computations to save power. The benefits of using the proposed MVM implementations techniques are demonstrated by comparing the proposed design with conventional implementation. The proposed circuit is implemented on an FPGA. It shows significant power and performance improvements compared to the conventional designs implemented on the same FPGA.