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8-bit floating-point representation

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Problem Detail: 

I'm studying about representing fractional numbers as floating-point values. It is going to be an 8-bit representation. Somewhere in the text, it is said that:

8-bit floating-point representation

"We use the first bit to represent the sign (1 for negative, 0 for positive), the next four bits for the sum of 7 and the actual exponent (we add 7 to allow for negative exponents), and the last three bits for the mantissa's fractional part"

Now the question is: Why "7" -and not another value- must be added to the actual exponent ?

Asked By : Peter
Answered By : adrianN

With 4 bits you can represent 16 different values: 0,1,...,15. If you want to allow negative exponents it makes sense to take (approximately) half of the possible values to mean a negative exponent. By adding 7 to the exponent you map the values -7,-6,...,0,1,...,8 to the representable range. You might also want to look up two's complement.

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