Numerical Methods, Binary, and finding two nearby machine numbers
$begingroup$
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 Jan 4 at 21:56
Rafa Budría
5,7151825
asked Jan 4 at 21:39
Mitul SuchakMitul Suchak
65
$endgroup$
add a comment |
$begingroup$
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 Jan 4 at 21:56
Rafa Budría
5,7151825
asked Jan 4 at 21:39
Mitul SuchakMitul Suchak
65
$endgroup$
add a comment |
$begingroup$
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 Jan 4 at 21:56
Rafa Budría
5,7151825
asked Jan 4 at 21:39
Mitul SuchakMitul Suchak
65
$endgroup$
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 Jan 4 at 21:56
Rafa Budría
5,7151825
asked Jan 4 at 21:39
Mitul SuchakMitul Suchak
65
edited Jan 4 at 21:56
Rafa Budría
5,7151825
asked Jan 4 at 21:39
Mitul SuchakMitul Suchak
65
edited Jan 4 at 21:56
Rafa Budría
5,7151825
edited Jan 4 at 21:56
Rafa Budría
5,7151825
edited Jan 4 at 21:56
Rafa Budría
5,7151825
5,7151825
asked Jan 4 at 21:39
Mitul SuchakMitul Suchak
65
asked Jan 4 at 21:39
Mitul SuchakMitul Suchak
65
asked Jan 4 at 21:39
Mitul SuchakMitul Suchak
65
65
add a comment |
add a comment |
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