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In this era of Transformers enjoying remarkable success, Convolutional Neural Networks (CNNs) remain highly relevant and useful. Indeed, hybrid Transformer-CNN network architectures, which combine the benefits of both approaches, have achieved impressive results. Vision Transformer (ViT) is a significant neural network architecture that features a convolutional layer as its first layer, primarily built on the transformer framework. However, owing to the distinct computation patterns inherent in attention and convolution, existing hardware accelerators for these two models are typically designed separately and lack a unified approach toward accelerating both models efficiently. In this paper, we present a dedicated accelerator on a field-programmable gate array (FPGA) platform. The accelerator, which integrates a configurable three-dimensional systolic array, is specifically designed to accelerate the inferential capabilities of hybrid Transformer-CNN networks. The Convolution and Transformer computations can be mapped to a systolic array by unifying these operations for matrix multiplication. Softmax and LayerNorm which are frequently used in hybrid Transformer-CNN networks were also implemented on FPGA boards. The accelerator achieved high performance with a peak throughput of 722 GOP/s at an average energy efficiency of 53 GOPS/W. Its respective computation latencies were 51.3 ms, 18.1 ms, and 6.8 ms for ViT-Base, ViT-Small, and ViT-Tiny. The accelerator provided a 12 × improvement in energy efficiency compared to the CPU, a 2. 3 × improvement compared to the GPU, and a 1. 5 × to 2 × improvement compared to existing accelerators regarding speed and energy efficiency. [ABSTRACT FROM AUTHOR]