CNNs have been shown to maintain reasonable classification accuracy when quantized to lower precisions. Quantizing to sub 8-bit activations and weights can result in accuracy falling below an acceptable threshold. Techniques exist for closing the accuracy gap of limited numeric precision typically by increasing computation. This results in a trade-off between throughput and accuracy and can be tailored for different networks through various combinations of activation and weight data widths. Hardware architectures like FPGAs provide the opportunity for data width specific computation through unique logic configurations leading to highly optimized processing that is unattainable by full precision networks. Ternary and binary weighted networks offer an efficient method of inference for 2-bit and 1-bit data respectively. Most hardware architectures can take advantage of the memory storage and bandwidth savings that come along with smaller datapaths, but very few architectures can take advantage of limited numeric precision at the computation level. In this paper, we present a hardware design for FPGAs that takes advantage of bandwidth, memory, power, and computation savings of limited numerical precision data. We provide insights into the trade-offs between throughput and accuracy for various networks and how they map to our framework. Further, we show how limited numeric precision computation can be efficiently mapped onto FPGAs for both ternary and binary cases. Starting with Arria 10, we show a 2-bit activation and ternary weighted AlexNet running in hardware that achieves 3,700 images per second on the ImageNet dataset with a top-1 accuracy of 0.49. Using a hardware modeler designed for our low numeric precision framework we project performance most notably for a 55.5 TOPS Stratix 10 device running a modified ResNet-34 with only 3.7% accuracy degradation compared with single precision.