x = 0.5 (with bit pattern 0x3f000000)
y = 0.25 (with bit pattern 0x3e800000)
then
x+y = 0.75 (with bit pattern 0x3f400000)
But if we just added the bit patterns like integers, we would get 0x7d800000 (with a float value of over 10^37). Just because they are discrete doesn't mean they are integers only that they can be mapped one-to-one with integers. The bit pattern is not the semantic meaning of the value, and you cannot perform correct operations if you ignore the semantics.
