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Comment by danielheath
I know someone working in this direction; they've described the big challenges as:
The big advantage is that instead of using 16 wires to represent a float16, you use the voltage on 1 wire to represent that number (which plausibly has far more precision than a float32). Additionally, you can e.g. wire two values directly together rather than loading numbers into an ALU, so the die space & power savings are potentially many, many orders of magnitude.