At 4 bits, you could just have a hard-wired table lookup. Two 4 bit values in, 256 entry table. You can have saturating arithmetic and a post-processing function for free. Somebody must be building hardware like that.

Low level software engineers use look up tables.

Hardware engineers realise that a compiler will almost always find some combination of gates which is smaller/faster than the contents of any table.

A LUT is pretty wasteful. You only have a one bit significand, so the mantissa and sign bits are boolean binops, and the exponent is a 2 bit adder.

and so you can at 1-bit too, and the hardware will be even smaller and cheaper