Numerical Methods, Binary, and finding two nearby machine numbers
I have the question,
Find the binary form of the number x = 2/7
Suppose that the number x = 2/7 is stored in a 32-bit computer.
Find the two nearby machine numbers $x−$ and $x+$. Which of the two machine numbers is taken to be the floating point representation, $fl(x)$, of $x$? What are the absolute and the relative roundoff errors in representing $x$ by $fl(x)$?
I know how to do the steps, the issue im having is when calculating the machine numbers, $x+$ and $x-$, to calculate $fl(x)$ my binary form is correct but I feel I am converting back incorrectly.
e.g for $x-(x-)$ the binary form is $(1.0010010010010...) ·2^{-26}$
I need to convert this into decimal/fractional form to compare with $(x+) - x$, which should be $mathbf{4/7 ·2^{-25}}$. It seems I can't get the answer.
binary
edited yesterday
Rafa Budría
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asked yesterday
Mitul Suchak
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I have the question,
Find the binary form of the number x = 2/7
Suppose that the number x = 2/7 is stored in a 32-bit computer.
Find the two nearby machine numbers $x−$ and $x+$. Which of the two machine numbers is taken to be the floating point representation, $fl(x)$, of $x$? What are the absolute and the relative roundoff errors in representing $x$ by $fl(x)$?
I know how to do the steps, the issue im having is when calculating the machine numbers, $x+$ and $x-$, to calculate $fl(x)$ my binary form is correct but I feel I am converting back incorrectly.
e.g for $x-(x-)$ the binary form is $(1.0010010010010...) ·2^{-26}$
I need to convert this into decimal/fractional form to compare with $(x+) - x$, which should be $mathbf{4/7 ·2^{-25}}$. It seems I can't get the answer.
binary
edited yesterday
Rafa Budría
5,5751825
asked yesterday
Mitul Suchak
13
New contributor
Mitul Suchak is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
I have the question,
Find the binary form of the number x = 2/7
Suppose that the number x = 2/7 is stored in a 32-bit computer.
Find the two nearby machine numbers $x−$ and $x+$. Which of the two machine numbers is taken to be the floating point representation, $fl(x)$, of $x$? What are the absolute and the relative roundoff errors in representing $x$ by $fl(x)$?
I know how to do the steps, the issue im having is when calculating the machine numbers, $x+$ and $x-$, to calculate $fl(x)$ my binary form is correct but I feel I am converting back incorrectly.
e.g for $x-(x-)$ the binary form is $(1.0010010010010...) ·2^{-26}$
I need to convert this into decimal/fractional form to compare with $(x+) - x$, which should be $mathbf{4/7 ·2^{-25}}$. It seems I can't get the answer.
binary
edited yesterday
Rafa Budría
5,5751825
asked yesterday
Mitul Suchak
13
New contributor
Mitul Suchak is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I have the question,
Find the binary form of the number x = 2/7
Suppose that the number x = 2/7 is stored in a 32-bit computer.
Find the two nearby machine numbers $x−$ and $x+$. Which of the two machine numbers is taken to be the floating point representation, $fl(x)$, of $x$? What are the absolute and the relative roundoff errors in representing $x$ by $fl(x)$?
I know how to do the steps, the issue im having is when calculating the machine numbers, $x+$ and $x-$, to calculate $fl(x)$ my binary form is correct but I feel I am converting back incorrectly.
e.g for $x-(x-)$ the binary form is $(1.0010010010010...) ·2^{-26}$
I need to convert this into decimal/fractional form to compare with $(x+) - x$, which should be $mathbf{4/7 ·2^{-25}}$. It seems I can't get the answer.
binary
binary
edited yesterday
Rafa Budría
5,5751825
asked yesterday
Mitul Suchak
13
New contributor
Mitul Suchak is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited yesterday
Rafa Budría
5,5751825
asked yesterday
Mitul Suchak
13
New contributor
Mitul Suchak is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited yesterday
Rafa Budría
5,5751825
edited yesterday
Rafa Budría
5,5751825
edited yesterday
Rafa Budría
5,5751825
5,5751825
asked yesterday
Mitul Suchak
13
New contributor
Mitul Suchak is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
Mitul Suchak
13
asked yesterday
Mitul Suchak
13
13
New contributor
Mitul Suchak is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Mitul Suchak is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Mitul Suchak is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
add a comment |
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