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01 ·Computer Architecture·★ MEMBER·PAPER·10 min read Systolic Arrays — Building the Heart of the TPU From Scratch Piling on multipliers doesn't make a chip faster, because moving data costs more than the arithmetic does. This piece takes the grid at the center of the TPU — the systolic array — and shows exactly how it maps the triple loop of matrix multiplication onto rows, columns and clock ticks, from a 2×2 hand trace to a cycle-accurate simulator to the batch-size and shape rules you'll actually tune.