23-bit mantissa and 9-bit exponent range and precision
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I have the following problem which I would like to make sure that I understand correctly. So I would appreciate your help in this matter.
Some computers (such as IBM mainframes) used to implement real data
using a 23-bit mantissa and a 9-bit exponent. What precision and range
can we expect from real data on these machines?
My understanding:
This floating point system has the following representation:
S EEEEEEEEE MMMMMMMMMMMMMMMMMMMMMMM
with S being the sign bit, E being the exponent bits, and M the mantissa bits. Is it true, then, that this FP system would have the range of $-2^{255}cdot 2^{23}$ to $2^{255}cdot 2^{23}$?
As to this FP's precision, the smallest distance between numbers would be the distance between $2^{-256} cdot 2^{-22}$ and $2^{-256} cdot 2^{-21}$.
Is this correct?
computer-science binary computational-mathematics floating-point
asked Jan 11 at 23:00
sequencesequence
4,26331437
$endgroup$
add a comment |
$begingroup$
I have the following problem which I would like to make sure that I understand correctly. So I would appreciate your help in this matter.
Some computers (such as IBM mainframes) used to implement real data
using a 23-bit mantissa and a 9-bit exponent. What precision and range
can we expect from real data on these machines?
My understanding:
This floating point system has the following representation:
S EEEEEEEEE MMMMMMMMMMMMMMMMMMMMMMM
with S being the sign bit, E being the exponent bits, and M the mantissa bits. Is it true, then, that this FP system would have the range of $-2^{255}cdot 2^{23}$ to $2^{255}cdot 2^{23}$?
As to this FP's precision, the smallest distance between numbers would be the distance between $2^{-256} cdot 2^{-22}$ and $2^{-256} cdot 2^{-21}$.
Is this correct?
computer-science binary computational-mathematics floating-point
asked Jan 11 at 23:00
sequencesequence
4,26331437
$endgroup$
add a comment |
$begingroup$
I have the following problem which I would like to make sure that I understand correctly. So I would appreciate your help in this matter.
Some computers (such as IBM mainframes) used to implement real data
using a 23-bit mantissa and a 9-bit exponent. What precision and range
can we expect from real data on these machines?
My understanding:
This floating point system has the following representation:
S EEEEEEEEE MMMMMMMMMMMMMMMMMMMMMMM
with S being the sign bit, E being the exponent bits, and M the mantissa bits. Is it true, then, that this FP system would have the range of $-2^{255}cdot 2^{23}$ to $2^{255}cdot 2^{23}$?
As to this FP's precision, the smallest distance between numbers would be the distance between $2^{-256} cdot 2^{-22}$ and $2^{-256} cdot 2^{-21}$.
Is this correct?
computer-science binary computational-mathematics floating-point
asked Jan 11 at 23:00
sequencesequence
4,26331437
$endgroup$
I have the following problem which I would like to make sure that I understand correctly. So I would appreciate your help in this matter.
Some computers (such as IBM mainframes) used to implement real data
using a 23-bit mantissa and a 9-bit exponent. What precision and range
can we expect from real data on these machines?
My understanding:
This floating point system has the following representation:
S EEEEEEEEE MMMMMMMMMMMMMMMMMMMMMMM
with S being the sign bit, E being the exponent bits, and M the mantissa bits. Is it true, then, that this FP system would have the range of $-2^{255}cdot 2^{23}$ to $2^{255}cdot 2^{23}$?
As to this FP's precision, the smallest distance between numbers would be the distance between $2^{-256} cdot 2^{-22}$ and $2^{-256} cdot 2^{-21}$.
Is this correct?
computer-science binary computational-mathematics floating-point
computer-science binary computational-mathematics floating-point
asked Jan 11 at 23:00
sequencesequence
4,26331437
asked Jan 11 at 23:00
sequencesequence
4,26331437
asked Jan 11 at 23:00
sequencesequence
4,26331437
asked Jan 11 at 23:00
sequencesequence
4,26331437
asked Jan 11 at 23:00
sequencesequence
4,26331437
4,26331437
add a comment |
add a comment |
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