It's technically not 1-bit, but 2-bit.
Anyway, I wonder if there is some HW support in modern CPUs/GPUs for linear algebra (like matrix multiplication) over Z_2^n ? I think it would be useful for SAT solving.
Or, technically, 1.58 bit. ;-)
not CPU/GPU but on FPGA finite field arithmetic is a thing; plenty of stuff like this around https://ieeexplore.ieee.org/document/4392002
There's carry-less multiplication (https://en.m.wikipedia.org/wiki/CLMUL_instruction_set), introduced by Intel in 2010.