The Converter Eats the Savings: System Energy of Memristor Crossbar Computing

Analogue memristor crossbars are quoted as performing a multiply-accumulate (MAC) at femtojoule energies inside the array. This paper prices the full operation at system level: the array (0.20 V read, 10 microsiemens mean conductance, 10 ns pulse: 4.00 fJ per MAC), the input digital-to-analogue converters, the output analogue-to-digital converters priced from the standard ADC survey figure of merit (present-day 30 fJ per conversion-step; best-reported 3 fJ per conversion-step; no projected converter), and write-and-verify programming (180 pJ per weight) amortised over the inferences reusing the weight, against the Horowitz ISSCC 2014 digital MAC (0.23 pJ at 8 bits). At 8 bits in a 128 by 128 array with present-day converters the system total is 70.18 fJ per MAC, 85.5% of it the output converter, so the 57.5-fold array-only advantage becomes 3.28-fold. The analogue system wins only above a crossover array size of about 10 rows at 4 bits, 37 rows at 8 bits, 263 rows at 12 bits and 2361 rows at 16 bits; at 16 bits it loses at any practical size. Weights reused fewer than about 1125 times also erase the 8-bit advantage. Model calculations are labelled SIMULATED, NOT MEASURED. The deposit includes the paper PDF and Markdown, the computation script (compute.py) that produces every number in the paper, and its outputs (results.json, results.txt).