Wouldn’t multiplication just be an 8 bit lookup table? a*b is just lut[a<<4+b]
A 256 element lookup table is much bigger than a simple multiplier
Multiplication at this resolution is already implemented via lookup tables.
For FP4, yes... sometimes... it depends. But newer Nvidia architecture eg Blackwell w/ NVFP4 does not, they perform micro block scaling in the core. For older architectures, low quants like FP4 are also often not done native, and instead inflated back to BF16, eg with BnB.
Specifically, you want to choose 16 values, all of which you can multiply an activation value by using circuitry which is as small as possible.