Earlier quoted context omitted.
I'll use custom notation =? ≤≥? x =? x = True Otherwise, a =? b = False NaN ≤≥? NaN = False Otherwise, a ≤≥? b = a =? b -1.0 ? b = b ? b | a ≤≥? b) In logic gates: For =?, bitwise equality. For ≤≥?, bitwise equality and a NaN detector. For ab I separate =? from ≤≥?. =? compares value, while ≤≥? compares order. NaN has no ordering, so it compares false. IEEE float only uses ≤≥? and names it ==.
It's better to first show truth tables, then K-maps, and only then logical formulas. But the main question is: does this FP2 have any real applications? Maybe it could be useful when only one operand is FP2? Especially for vectorized math.
If I had to guess, we could use this for a very compact output of the sign function. [-Inf,0) maps to -1.0, 0 maps to 0.0, (0,Inf] maps to +1.0, and NaN maps to NaN. I don't know what application would need the sign function, though. I haven't needed it yet in my programming experience.