Just wondering, would it be better to normalise like flooding point does and always include a virtual 1 on the front of the number? This encoding wastes space b

Just wondering, would it be better to normalise like flooding point does and always include a virtual 1 on the front of the number? This encoding wastes space because some numbers can be encoded multiple ways e.g. 3 and 6. On the other hand, that would mean zero couldn't be encoded, but you don't need a zero for most maths as it doesn't do anything (and you could use a zero register.) Edit to add: the even shift is a problem, but you could use 7 bits of number, 1 implicit leading 1 bit, and 5 bits to cover any 32-bit shift.