Quantized low-precision neural networks are very popular because they require less computational resources for inference and can provide high performance, which is vital for real-time and embedded recognition systems. However, their advantages are apparent for FPGA and ASIC devices, while general-purpose processor architectures are not always able to perform low-bit integer computations efficiently. The most frequently used low-precision neural network model for mobile central processors is an 8-bit quantized network. However, in a number of cases, it is possible to use fewer bits for weights and activations, and the only problem is the difficulty of efficient implementation. We introduce an efficient implementation of 4-bit matrix multiplication for quantized neural networks and perform time measurements on a mobile ARM processor. It shows 2.9 times speedup compared to standard floating-point multiplication and is 1.5 times faster than 8-bit quantized one. We also demonstrate a 4-bit quantized neural network for OCR recognition on the MIDV-500 dataset. 4-bit quantization gives 95.0% accuracy and 48% overall inference speedup, while an 8-bit quantized network gives 95.4% accuracy and 39% speedup. The results show that 4-bit quantization perfectly suits mobile devices, yielding good enough accuracy and low inference time.