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Convolutional Neural Networks (CNNs) demonstrate excellent performance in various applications but have high computational complexity. Quantization is applied to reduce the latency and storage cost of CNNs. Among the quantization methods, Binary and Ternary Weight Networks (BWNs and TWNs) have a unique advantage over 8-bit and 4-bit quantization. They replace the multiplication operations in CNNs with additions, which are favoured on In-Memory-Computing (IMC) devices. IMC acceleration for BWNs has been widely studied. However, though TWNs have higher accuracy and better sparsity than BWNs, IMC acceleration for TWNs has limited research. TWNs on existing IMC devices are inefficient because the sparsity is not well utilized, and the addition operation is not efficient. In this paper, we propose FAT as a novel IMC accelerator for TWNs. First, we propose a Sparse Addition Control Unit, which utilizes the sparsity of TWNs to skip the null operations on zero weights. Second, we propose a fast addition scheme based on the memory Sense Amplifier to avoid the time overhead of both carry propagation and writing back the carry to memory cells. Third, we further propose a Combined-Stationary data mapping to reduce the data movement of activations and weights and increase the parallelism across memory columns. Simulation results show that for addition operations at the Sense Amplifier level, FAT achieves 2.00X speedup, 1.22X power efficiency, and 1.22X area efficiency compared with a State-Of-The-Art IMC accelerator ParaPIM. FAT achieves 10.02X speedup and 12.19X energy efficiency compared with ParaPIM on networks with 80% average sparsity.