Unary computing, whose arithmetics require only one logic gate, has enabled efficient DNN processing, especially on strictly power-constrained devices. However, unary computing still confronts the power efficiency bottleneck for buffering unary bitstreams. The buffering of unary bitstreams requires accumulating bits into large bitwidth binary numbers. The large bitwidth binary number needs to activate all bits per cycle in case of carry propagation. As a result, the accumulation process accounts for 32%-70% of the power budget.To push the boundary of power efficiency, we propose Cambricon-U, a systolic random increment memory architecture featuring efficient accumulation. By leveraging skew number data format, Cambricon-U only activates no more than three bits (instead of all bits) from each number per accumulating cycle. Experimental results show that Cambricon-U reduces 51% power on unary accumulation, and improves 1.18-1.45× energy efficiency over uSystolic, the SOTA unary computing scheme baseline, with -1.9%~ +0.77% area overhead.CCS CONCEPTS• Computer systems organization → Architectures; • Hardware → Emerging architectures.