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Studying for A level computing we are repeatedly told that a negative normalised floating point binary number is not normalised if it starts with 11 by textbooks, exam questions and teachers.

In the case of minus 11 in twos compliment it can be written as 10101 and so the number in normalised form would be 10101 00100 this follows the rule of no 11 at the beginning of the number

But for minus 1 the twos compliment version is 11111 and so what would the normalised version 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 the number begin with 11 and how would minus one be represented with an explanation?

Tristan Warren
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  • What's the exact floating point format? It can't be IEEE 754 (doesn't use two's complement and doesn't specify 10 bit formats), so please explain which bits encode which values (sign, exponent, significand) and how (sign/magnitude vs two's complement, offset-bias vs two's complement, etc.). –  May 11 '15 at 22:28
  • I don't know, they don't specify on the course, I don't think it is anything specific. The numbers are represented with 5 bits for the exponent and 5 bits for the mantissa and both use twos compliment, sorry I can't be of more help – Tristan Warren May 11 '15 at 22:35
  • Together with your examples, I think I understand the format now. Unfortunately I don't see how it could be that negative normalized numbers can't start with 10. Have you asked the teachers? –  May 11 '15 at 22:43
  • The teachers read from the books and exam papers and don't really know much about it themselves, if the mantissa was allowed extra bits would this solve the problem? – Tristan Warren May 12 '15 at 19:24

1 Answers1

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

The problem with this type of maths is that no one really does it. So you're going to find it hard to find any "experts" in this field. The 0.1 and 1.0 rules 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 accuracy as possible within the boundaries you are given. So if you were to make the exponent 0010 which complies with your rule... 1.010 0010 you are loosing accuracy (not in the case of -1) but the potential is there.

Matt Rowe
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