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We propose Sectored DRAM, a new, low-overhead DRAM substrate that reduces wasted energy by enabling fine-grained DRAM data transfers and DRAM row activation. Sectored DRAM leverages two key ideas to enable fine-grained data transfers and row activation at low chip area cost. First, a cache block transfer between main memory and the memory controller happens in a fixed number of clock cycles where only a small portion of the cache block (a word) is transferred in each cycle. Sectored DRAM augments the memory controller and the DRAM chip to execute cache block transfers in a variable number of clock cycles based on the workload access pattern with minor modifications to the memory controller's and the DRAM chip's circuitry. Second, a large DRAM row, by design, is already partitioned into smaller independent physically isolated regions. Sectored DRAM provides the memory controller with the ability to activate each such region based on the workload access pattern via small modifications to the DRAM chip's array access circuitry. Activating smaller regions of a large row relaxes DRAM power delivery constraints and allows the memory controller to schedule DRAM accesses faster. Compared to a system with coarse-grained DRAM, Sectored DRAM reduces the DRAM energy consumption of highly-memory-intensive workloads by up to (on average) 33% (20%) while improving their performance by up to (on average) 36% (17%). Sectored DRAM's DRAM energy savings, combined with its system performance improvement, allows system-wide energy savings of up to 23%. Sectored DRAM's DRAM chip area overhead is 1.7% the area of a modern DDR4 chip. We hope and believe that Sectored DRAM's ideas and results will help to enable more efficient and high-performance memory systems. To this end, we open source Sectored DRAM at https://github.com/CMU-SAFARI/Sectored-DRAM.