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This paper presents a technique for eliminating redundant cache-tag and cache-way accesses to reduce power consumption. The basic idea is to keep a small number of most recently used (MRU) addresses in a memory address buffer (MAB) and to omit redundant tag and way accesses when there is a MAB-hit. Since the approach keeps only tag and set-index values in the MAB, the energy and area overheads are relatively small even for a MAB with a large number of entries. Furthermore, the approach does not sacrifice the performance. In other words, neither the cycle time nor the number of executed cycles increases. The proposed technique has been applied to the Fujitsu VLIW processor (FR-V) and its power saving has been estimated using NanoSim. Experiments for 32 kB 2-way set associative caches show the power consumption of I-cache and D-cache can be reduced by 40% and 50%, respectively.