Mixing
How to rewrite a decimal number $x$ as $1.ycdot2^{n}$?
$begingroup$
If I have a number, let's say "$-77,51$", what is a good way to rewrite it as $1.ycdot 2^{n}$?
elementary-number-theory binary
asked Jan 22 at 21:30
KevinKevin
16211
$endgroup$
add a comment |
$begingroup$
If I have a number, let's say "$-77,51$", what is a good way to rewrite it as $1.ycdot 2^{n}$?
elementary-number-theory binary
asked Jan 22 at 21:30
KevinKevin
16211
$endgroup$
$begingroup$
What do you mean by "write it as a product of $2^n$? Do you want it to be written as $x cdot 2^n$ where $|x|<2$?
$endgroup$
– kccu
Jan 22 at 21:33
$begingroup$
The question does not make sense.
$endgroup$
– copper.hat
Jan 22 at 21:34
$begingroup$
@kccu Let me clarify. Let's say that I have a number $−77,51$, it can also be written as $−1,21...∗2^6$. What is a good way to write any decimal number in that form?
$endgroup$
– Kevin
Jan 22 at 21:39
$begingroup$
@Kevin It is unclear what you mean by "in that form". For instance, if your number is $12$, should I write $1.5 cdot 2^3$? Or is $3 cdot 2^2$ acceptable? What about $0.75 cdot 2^4$? You haven't precisely said what you mean.
$endgroup$
– kccu
Jan 22 at 21:42
$begingroup$
@kccu I'm sorry, you're right. I should've specified. The form is $1.y cdot 2^n$.
$endgroup$
– Kevin
Jan 22 at 21:43
add a comment |
$begingroup$
If I have a number, let's say "$-77,51$", what is a good way to rewrite it as $1.ycdot 2^{n}$?
elementary-number-theory binary
asked Jan 22 at 21:30
KevinKevin
16211
$endgroup$
If I have a number, let's say "$-77,51$", what is a good way to rewrite it as $1.ycdot 2^{n}$?
elementary-number-theory binary
elementary-number-theory binary
asked Jan 22 at 21:30
KevinKevin
16211
asked Jan 22 at 21:30
KevinKevin
16211
edited Jan 22 at 21:44
Kevin
asked Jan 22 at 21:30
KevinKevin
16211
asked Jan 22 at 21:30
KevinKevin
16211
asked Jan 22 at 21:30
KevinKevin
16211
16211
$begingroup$
What do you mean by "write it as a product of $2^n$? Do you want it to be written as $x cdot 2^n$ where $|x|<2$?
$endgroup$
– kccu
Jan 22 at 21:33
$begingroup$
The question does not make sense.
$endgroup$
– copper.hat
Jan 22 at 21:34
$begingroup$
@kccu Let me clarify. Let's say that I have a number $−77,51$, it can also be written as $−1,21...∗2^6$. What is a good way to write any decimal number in that form?
$endgroup$
– Kevin
Jan 22 at 21:39
$begingroup$
@Kevin It is unclear what you mean by "in that form". For instance, if your number is $12$, should I write $1.5 cdot 2^3$? Or is $3 cdot 2^2$ acceptable? What about $0.75 cdot 2^4$? You haven't precisely said what you mean.
$endgroup$
– kccu
Jan 22 at 21:42
$begingroup$
@kccu I'm sorry, you're right. I should've specified. The form is $1.y cdot 2^n$.
$endgroup$
– Kevin
Jan 22 at 21:43
add a comment |
$begingroup$
What do you mean by "write it as a product of $2^n$? Do you want it to be written as $x cdot 2^n$ where $|x|<2$?
$endgroup$
– kccu
Jan 22 at 21:33
$begingroup$
The question does not make sense.
$endgroup$
– copper.hat
Jan 22 at 21:34
$begingroup$
@kccu Let me clarify. Let's say that I have a number $−77,51$, it can also be written as $−1,21...∗2^6$. What is a good way to write any decimal number in that form?
$endgroup$
– Kevin
Jan 22 at 21:39
$begingroup$
@Kevin It is unclear what you mean by "in that form". For instance, if your number is $12$, should I write $1.5 cdot 2^3$? Or is $3 cdot 2^2$ acceptable? What about $0.75 cdot 2^4$? You haven't precisely said what you mean.
$endgroup$
– kccu
Jan 22 at 21:42
$begingroup$
@kccu I'm sorry, you're right. I should've specified. The form is $1.y cdot 2^n$.
$endgroup$
– Kevin
Jan 22 at 21:43
$begingroup$
What do you mean by "write it as a product of $2^n$? Do you want it to be written as $x cdot 2^n$ where $|x|<2$?
$endgroup$
– kccu
Jan 22 at 21:33
$begingroup$
What do you mean by "write it as a product of $2^n$? Do you want it to be written as $x cdot 2^n$ where $|x|<2$?
$endgroup$
– kccu
Jan 22 at 21:33
$begingroup$
The question does not make sense.
$endgroup$
– copper.hat
Jan 22 at 21:34
$begingroup$
The question does not make sense.
$endgroup$
– copper.hat
Jan 22 at 21:34
$begingroup$
@kccu Let me clarify. Let's say that I have a number $−77,51$, it can also be written as $−1,21...∗2^6$. What is a good way to write any decimal number in that form?
$endgroup$
– Kevin
Jan 22 at 21:39
$begingroup$
@kccu Let me clarify. Let's say that I have a number $−77,51$, it can also be written as $−1,21...∗2^6$. What is a good way to write any decimal number in that form?
$endgroup$
– Kevin
Jan 22 at 21:39
$begingroup$
@Kevin It is unclear what you mean by "in that form". For instance, if your number is $12$, should I write $1.5 cdot 2^3$? Or is $3 cdot 2^2$ acceptable? What about $0.75 cdot 2^4$? You haven't precisely said what you mean.
$endgroup$
– kccu
Jan 22 at 21:42
$begingroup$
@Kevin It is unclear what you mean by "in that form". For instance, if your number is $12$, should I write $1.5 cdot 2^3$? Or is $3 cdot 2^2$ acceptable? What about $0.75 cdot 2^4$? You haven't precisely said what you mean.
$endgroup$
– kccu
Jan 22 at 21:42
$begingroup$
@kccu I'm sorry, you're right. I should've specified. The form is $1.y cdot 2^n$.
$endgroup$
– Kevin
Jan 22 at 21:43
$begingroup$
@kccu I'm sorry, you're right. I should've specified. The form is $1.y cdot 2^n$.
$endgroup$
– Kevin
Jan 22 at 21:43
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Given your number $n$, take $log_2 (|n|)$ and round down to the next smaller integer. That gives you the power of $2$ you want to have the rest be between $1$ and $2$. In your example, $log_2 (77.51)approx 6.276$ so the exponent is $6$. Then $2^6=64$, so divide your number by $64$. $frac {77.51}{64}approx 1.2111$
answered Jan 22 at 21:41
Ross MillikanRoss Millikan
299k24200374
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add a comment |
$begingroup$
$$x = frac{x}{lfloor{log_2 x}rfloor}cdot {lfloor{log_2 x}rfloor},quad x>0$$
answered Jan 22 at 21:40
rogerlrogerl
18k22748
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add a comment |
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2 Answers
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2 Answers
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$begingroup$
Given your number $n$, take $log_2 (|n|)$ and round down to the next smaller integer. That gives you the power of $2$ you want to have the rest be between $1$ and $2$. In your example, $log_2 (77.51)approx 6.276$ so the exponent is $6$. Then $2^6=64$, so divide your number by $64$. $frac {77.51}{64}approx 1.2111$
answered Jan 22 at 21:41
Ross MillikanRoss Millikan
299k24200374
$endgroup$
add a comment |
$begingroup$
Given your number $n$, take $log_2 (|n|)$ and round down to the next smaller integer. That gives you the power of $2$ you want to have the rest be between $1$ and $2$. In your example, $log_2 (77.51)approx 6.276$ so the exponent is $6$. Then $2^6=64$, so divide your number by $64$. $frac {77.51}{64}approx 1.2111$
answered Jan 22 at 21:41
Ross MillikanRoss Millikan
299k24200374
$endgroup$
add a comment |
$begingroup$
Given your number $n$, take $log_2 (|n|)$ and round down to the next smaller integer. That gives you the power of $2$ you want to have the rest be between $1$ and $2$. In your example, $log_2 (77.51)approx 6.276$ so the exponent is $6$. Then $2^6=64$, so divide your number by $64$. $frac {77.51}{64}approx 1.2111$
answered Jan 22 at 21:41
Ross MillikanRoss Millikan
299k24200374
$endgroup$
Given your number $n$, take $log_2 (|n|)$ and round down to the next smaller integer. That gives you the power of $2$ you want to have the rest be between $1$ and $2$. In your example, $log_2 (77.51)approx 6.276$ so the exponent is $6$. Then $2^6=64$, so divide your number by $64$. $frac {77.51}{64}approx 1.2111$
answered Jan 22 at 21:41
Ross MillikanRoss Millikan
299k24200374
answered Jan 22 at 21:41
Ross MillikanRoss Millikan
299k24200374
answered Jan 22 at 21:41
Ross MillikanRoss Millikan
299k24200374
answered Jan 22 at 21:41
Ross MillikanRoss Millikan
299k24200374
299k24200374
add a comment |
add a comment |
$begingroup$
$$x = frac{x}{lfloor{log_2 x}rfloor}cdot {lfloor{log_2 x}rfloor},quad x>0$$
answered Jan 22 at 21:40
rogerlrogerl
18k22748
$endgroup$
add a comment |
$begingroup$
$$x = frac{x}{lfloor{log_2 x}rfloor}cdot {lfloor{log_2 x}rfloor},quad x>0$$
answered Jan 22 at 21:40
rogerlrogerl
18k22748
$endgroup$
add a comment |
$begingroup$
$$x = frac{x}{lfloor{log_2 x}rfloor}cdot {lfloor{log_2 x}rfloor},quad x>0$$
answered Jan 22 at 21:40
rogerlrogerl
18k22748
$endgroup$
$$x = frac{x}{lfloor{log_2 x}rfloor}cdot {lfloor{log_2 x}rfloor},quad x>0$$
answered Jan 22 at 21:40
rogerlrogerl
18k22748
answered Jan 22 at 21:40
rogerlrogerl
18k22748
answered Jan 22 at 21:40
rogerlrogerl
18k22748
answered Jan 22 at 21:40
rogerlrogerl
18k22748
18k22748
add a comment |
add a comment |
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$begingroup$
What do you mean by "write it as a product of $2^n$? Do you want it to be written as $x cdot 2^n$ where $|x|<2$?
$endgroup$
– kccu
Jan 22 at 21:33
$begingroup$
The question does not make sense.
$endgroup$
– copper.hat
Jan 22 at 21:34
$begingroup$
@kccu Let me clarify. Let's say that I have a number $−77,51$, it can also be written as $−1,21...∗2^6$. What is a good way to write any decimal number in that form?
$endgroup$
– Kevin
Jan 22 at 21:39
$begingroup$
@Kevin It is unclear what you mean by "in that form". For instance, if your number is $12$, should I write $1.5 cdot 2^3$? Or is $3 cdot 2^2$ acceptable? What about $0.75 cdot 2^4$? You haven't precisely said what you mean.
$endgroup$
– kccu
Jan 22 at 21:42
$begingroup$
@kccu I'm sorry, you're right. I should've specified. The form is $1.y cdot 2^n$.
$endgroup$
– Kevin
Jan 22 at 21:43