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I am trying to build a class where user can compute some floating operations with accuracy provided. Example : User want to have up to 4 numbers accuracy thus everything less than 0.0001 is zero and bigger than 9999 is inf.

I think best way is to create bit (or maybe byte) array to store sign, mantissa and exponent. For this "4 (decimal) numbers accuracy" I could calculate how many bits I need to store smallest and biggest value and then create array of such size.

This leaded me to two of my questions :

1. Why single precision has exactly 8 bits for exponent and 24 for mantissa (IEEE 754) not 10 and 53 nor 12 and 51? Is it some how relevant or is it just agreement?
2. Assuming I need 4 digit precision for 9999 it is 14 bits but how much space do I need to keep 0.0001 in 4 (decimal) digit accuracy?

If an answer for 1st question is "it is just agreement" I have yet another question :

• How do I choose the best exponent and mantissa for my problem?

Please disregard that numbers bigger and smaller might be calculated here ( I will just 'if' it out), but I do not want to use double/float/etc for this I need as much "space"(meaning bigger than double) for numbers as I possibly can and save space ( I dont want to create too big array).

I hope this is not duplicate of any question - I couldnt find anything like this on google.

I am trying to build a class where user can compute floating operations with a particular accuracy. For example, if the user wants to have up to 4 digit accuracy, everything less than 0.0001 is zero and everything bigger than 9999 is inf.

I think the best way is to create a bit (or maybe byte) array to store sign, mantissa and exponent. For istance, with 4 (decimal) digits accuracy I could calculate how many bits I would need to store smallest and biggest value and then create array of that size.

This leads me to two of my questions :

1. Why does single precision use exactly 8 bits for the exponent and 24 for the mantissa (IEEE 754) rather than 10 and 53, or 12 and 51? Is it somehow relevant or is it just a standard?
2. Assuming I need 4 digit precision for 9999, I would need 14 bits but how much space do I need to keep 0.0001 in 4 (decimal) digit accuracy?

If the answer for the 1st question is "it is just a standard" I have yet another question :

• How do I choose the best exponent and mantissa for my problem?

Please disregard the fact numbers bigger and smaller might be calculated here as I will just 'if' them out. I do not want to use double/float/etc for this I need as I expect to use more memory than a double would need but I do not want to use too much space.

I am trying to build a class where user can compute some floating operations with accuracy provided. Example : User want to have up to 4 numbers accuracy thus everything less than 0.0001 is zero and bigger than 9999.9999 is inf.

I think best way is to create bit (or maybe byte) array to store sign, mantissa and exponent. For this "4 (decimal) numbers accuracy" I could calculate how many bits I need to store smallest and biggest value and then create array of such size.

This leaded me to two of my questions :

1. Why single precision has exactly 8 bits for exponent and 24 for mantissa (IEEE 754) not 10 and 53 nor 12 and 51? Is it some how relevant or is it just agreement?
2. Assuming I need 4 digit precision for 9999 it is 14 bits but how much space do I need to keep 0.0001 in 4 (decimal) digit accuracy?

If an answer for 1st question is "it is just agreement" I have yet another question :

• How do I choose the best exponent and mantissa for my problem?

Please disregard that numbers bigger and smaller might be calculated here ( I will just 'if' it out), but I do not want to use double/float/etc for this I need as much "space"(meaning bigger than double) for numbers as I possibly can and save space ( I dont want to create too big array).

I hope this is not duplicate of any question - I couldnt find anything like this on google.

I am trying to build a class where user can compute some floating operations with accuracy provided. Example : User want to have up to 4 numbers accuracy thus everything less than 0.0001 is zero and bigger than 9999 is inf.

I think best way is to create bit (or maybe byte) array to store sign, mantissa and exponent. For this "4 (decimal) numbers accuracy" I could calculate how many bits I need to store smallest and biggest value and then create array of such size.

This leaded me to two of my questions :

1. Why single precision has exactly 8 bits for exponent and 24 for mantissa (IEEE 754) not 10 and 53 nor 12 and 51? Is it some how relevant or is it just agreement?
2. Assuming I need 4 digit precision for 9999 it is 14 bits but how much space do I need to keep 0.0001 in 4 (decimal) digit accuracy?

If an answer for 1st question is "it is just agreement" I have yet another question :

• How do I choose the best exponent and mantissa for my problem?

Please disregard that numbers bigger and smaller might be calculated here ( I will just 'if' it out), but I do not want to use double/float/etc for this I need as much "space"(meaning bigger than double) for numbers as I possibly can and save space ( I dont want to create too big array).

I hope this is not duplicate of any question - I couldnt find anything like this on google.

I am trying to build a class where user can compute some floating operations with accuracy provided. Example : User want to have up to 4 numbers accuracy thus everything less than 0.0001 is zero and bigger than 9999 is inf.

I think best way is to create bit (or maybe byte) array to store sign, mantissa and exponent. For this "4 (decimal) numbers accuracy" I could calculate how many bits I need to store smallest and biggest value and then create array of such size.

This leaded me to two of my questions :

1. Why single precision has exactly 8 bits for exponent and 24 for mantissa (IEEE 754) not 10 and 53 nor 12 and 51? Is it some how relevant or is it just agreement?
2. Assuming I need 4 digit precision for 9999 it is 14 bits but how much space do I need to keep 0.0001 in 4 (decimal) digit accuracy?

If an answer for 1st question is "it is just agreement" I have yet another question :

• How do I choose the best exponent and mantissa for my problem?

Please disregard that numbers bigger and smaller might be calculated here ( I will just 'if' it out), but I do not want to use double/float/etc for this I need as much "space"(meaning bigger than double) for numbers as I possibly can and save space ( I dont want to create too big array).

I hope this is not duplicate of any question - I couldnt find anything like this on google.

I am trying to build a class where user can compute some floating operations with accuracy provided. Example : User want to have up to 4 numbers accuracy thus everything less than 0.0001 is zero and bigger than 9999.9999 is inf.

I think best way is to create bit (or maybe byte) array to store sign, mantissa and exponent. For this "4 (decimal) numbers accuracy" I could calculate how many bits I need to store smallest and biggest value and then create array of such size.

This leaded me to two of my questions :

1. Why single precision has exactly 8 bits for exponent and 24 for mantissa (IEEE 754) not 10 and 53 nor 12 and 51? Is it some how relevant or is it just agreement?
2. Assuming I need 4 digit precision for 9999 it is 14 bits but how much space do I need to keep 0.0001 in 4 (decimal) digit accuracy?

If an answer for 1st question is "it is just agreement" I have yet another question :

• How do I choose the best exponent and mantissa for my problem?

Please disregard that numbers bigger and smaller might be calculated here ( I will just 'if' it out), but I do not want to use double/float/etc for this I need as much "space"(meaning bigger than double) for numbers as I possibly can and save space ( I dont want to create too big array).

I hope this is not duplicate of any question - I couldnt find anything like this on google.