Why does a negative normalized binary floating point number start at 11?

While studying level calculations, we are repeatedly told that a negative normalized binary floating point number is not normalized if it starts with 11 textbooks, exam questions, and teachers.

In the case of minus 11 in two compliments, it can be written as 10101, so the number in normalized form would be 10101 00100, this follows rule # 11 at the beginning of the number

But for minus 1, the twos compliment version is 11111, and so as the normalized version would be, 11111 00100 works, but breaks the rule, 011111 00101 makes the number positive and uses too many bits, 10111 00100 makes minus 9 instead of minus 1

Basically, why can't a number start at 11 and how will less than one explanation be presented?


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You are correct, the normalized version -1 in binary is 1.100 0001

The problem with this type of math is that nobody else does it. Therefore, it will be difficult for you to find "experts" in this field. Rules 0.1 and 1.0 are useful for learning the concept. However, conceptual rules don't always apply in the real world. The point of normalization is to maintain as much precision as possible within the bounds you give. So if you were to make an exponent 0010 that matches your rule ... 1.010 0010, you lose precision (not in the case of -1), but there is potential.



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