Converting Base 16 digits to base 2 and 10 - Analysis Question
$begingroup$
With base $16$, the digits are denoted as $0, 1,ldots, 9, A,ldots, F$. Let $n = AB3$. Rewrite $n$ with bases $10$, $2$.
I have no clue what this question means and how I should attempt to do this.
number-systems
$endgroup$
add a comment |
$begingroup$
With base $16$, the digits are denoted as $0, 1,ldots, 9, A,ldots, F$. Let $n = AB3$. Rewrite $n$ with bases $10$, $2$.
I have no clue what this question means and how I should attempt to do this.
number-systems
$endgroup$
$begingroup$
If you understand radix notation (binary, hexadecimal, decimal) then the Question is rather straightforward. You are being given the hexadecimal presentation of a number, and asked re-present the same number as binary and decimal expressions.
$endgroup$
– hardmath
Nov 21 '13 at 14:03
add a comment |
$begingroup$
With base $16$, the digits are denoted as $0, 1,ldots, 9, A,ldots, F$. Let $n = AB3$. Rewrite $n$ with bases $10$, $2$.
I have no clue what this question means and how I should attempt to do this.
number-systems
$endgroup$
With base $16$, the digits are denoted as $0, 1,ldots, 9, A,ldots, F$. Let $n = AB3$. Rewrite $n$ with bases $10$, $2$.
I have no clue what this question means and how I should attempt to do this.
number-systems
number-systems
edited Jan 9 at 23:35
trw
3331311
3331311
asked Nov 21 '13 at 13:57
Kasun JayasuriyaKasun Jayasuriya
144
144
$begingroup$
If you understand radix notation (binary, hexadecimal, decimal) then the Question is rather straightforward. You are being given the hexadecimal presentation of a number, and asked re-present the same number as binary and decimal expressions.
$endgroup$
– hardmath
Nov 21 '13 at 14:03
add a comment |
$begingroup$
If you understand radix notation (binary, hexadecimal, decimal) then the Question is rather straightforward. You are being given the hexadecimal presentation of a number, and asked re-present the same number as binary and decimal expressions.
$endgroup$
– hardmath
Nov 21 '13 at 14:03
$begingroup$
If you understand radix notation (binary, hexadecimal, decimal) then the Question is rather straightforward. You are being given the hexadecimal presentation of a number, and asked re-present the same number as binary and decimal expressions.
$endgroup$
– hardmath
Nov 21 '13 at 14:03
$begingroup$
If you understand radix notation (binary, hexadecimal, decimal) then the Question is rather straightforward. You are being given the hexadecimal presentation of a number, and asked re-present the same number as binary and decimal expressions.
$endgroup$
– hardmath
Nov 21 '13 at 14:03
add a comment |
3 Answers
3
active
oldest
votes
$begingroup$
Hint: a number $n$ in base 10 can be written as follow: $$n=a_i cdot 10^{i} + a_{i-1} cdot 10^{i-1} cdot dots cdot a_1 cdot 10 + a_0 cdot 10^0 $$ where $a_i in {0, 1, dots, 9}$. Similar to this case...
$endgroup$
$begingroup$
So what's i in this?
$endgroup$
– Kasun Jayasuriya
Nov 21 '13 at 14:10
$begingroup$
It is the number of the digit, counting from the right and starting with $0$. In base $10$, the $i=2$ digit is the hundreds digit (because we started counting with zero), and the value is $10^2$
$endgroup$
– Ross Millikan
Nov 21 '13 at 14:17
add a comment |
$begingroup$
In base 16, each number is composed of a series of the digits 0-9 and A-F, where, A represents 10, B 11, C 12 and so on up to the maximum for any digit which is F, representing 15.
As such, AB$3$ represents $10$ in the $16^2=256$s column, $11$ in the $16^1=16$s column and 3 in the units column, so in decimal (base 10) that's $10(256)+11(16)+3=2739$.
In general, for a natural number $n$, given a number in base $n$, the digit at the far right tells you how many units, the digit to the left of that how many $n$s, the next digit to the left how many $n^2$s etc. None of the digits in a number in base $n$ is allowed to exceed $n-1$.
For how to convert the number to base 2, see the algorithm presented in Adi Dani's answer.
$endgroup$
add a comment |
$begingroup$
$$n=(AB3)_{16}=Acdot16^2+Bcdot 16^1+3cdot 16^0=10cdot256+11cdot16+3cdot1=2739$$
$$2739:2=1369+1$$
$$1369:2=2cdot684+1$$
$$684:2=2cdot342+0$$
$$342:2=2cdot171+0$$
$$171:2=2cdot85+1$$
$$85:2=2cdot42+1$$
$$42:2=2cdot21+0$$
$$21:2=2cdot10+1$$
$$10:2=2cdot5+0$$
$$5:2=2cdot2+1$$
$$2=2cdot1+0$$
$$2739=(101010110011)_2$$
$endgroup$
$begingroup$
I gave you +1 without having checked your base 2 assertion, which is incorrect, but the algorithm is useful, so you deserve the +1. 110011001111 is not 2739 in base 2: it's 3279. $$110011001111=2048+1024+128+64+8+4+2+1=3279$$ The error is in the second line (and hence, as you know, all subsequent lines are inapplicable too), which should be $$1639=684⋅2+1$$
$endgroup$
– George Tomlinson
Nov 22 '13 at 20:43
1
$begingroup$
I edit my answer now is correct. I use $1639$ instead of $1369$ Thank you @bluesh34
$endgroup$
– Adi Dani
Nov 22 '13 at 22:34
$begingroup$
No problems. Oh, yeah: I meant 1369.
$endgroup$
– George Tomlinson
Nov 25 '13 at 17:54
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f575971%2fconverting-base-16-digits-to-base-2-and-10-analysis-question%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Hint: a number $n$ in base 10 can be written as follow: $$n=a_i cdot 10^{i} + a_{i-1} cdot 10^{i-1} cdot dots cdot a_1 cdot 10 + a_0 cdot 10^0 $$ where $a_i in {0, 1, dots, 9}$. Similar to this case...
$endgroup$
$begingroup$
So what's i in this?
$endgroup$
– Kasun Jayasuriya
Nov 21 '13 at 14:10
$begingroup$
It is the number of the digit, counting from the right and starting with $0$. In base $10$, the $i=2$ digit is the hundreds digit (because we started counting with zero), and the value is $10^2$
$endgroup$
– Ross Millikan
Nov 21 '13 at 14:17
add a comment |
$begingroup$
Hint: a number $n$ in base 10 can be written as follow: $$n=a_i cdot 10^{i} + a_{i-1} cdot 10^{i-1} cdot dots cdot a_1 cdot 10 + a_0 cdot 10^0 $$ where $a_i in {0, 1, dots, 9}$. Similar to this case...
$endgroup$
$begingroup$
So what's i in this?
$endgroup$
– Kasun Jayasuriya
Nov 21 '13 at 14:10
$begingroup$
It is the number of the digit, counting from the right and starting with $0$. In base $10$, the $i=2$ digit is the hundreds digit (because we started counting with zero), and the value is $10^2$
$endgroup$
– Ross Millikan
Nov 21 '13 at 14:17
add a comment |
$begingroup$
Hint: a number $n$ in base 10 can be written as follow: $$n=a_i cdot 10^{i} + a_{i-1} cdot 10^{i-1} cdot dots cdot a_1 cdot 10 + a_0 cdot 10^0 $$ where $a_i in {0, 1, dots, 9}$. Similar to this case...
$endgroup$
Hint: a number $n$ in base 10 can be written as follow: $$n=a_i cdot 10^{i} + a_{i-1} cdot 10^{i-1} cdot dots cdot a_1 cdot 10 + a_0 cdot 10^0 $$ where $a_i in {0, 1, dots, 9}$. Similar to this case...
answered Nov 21 '13 at 14:02
gangrenegangrene
915514
915514
$begingroup$
So what's i in this?
$endgroup$
– Kasun Jayasuriya
Nov 21 '13 at 14:10
$begingroup$
It is the number of the digit, counting from the right and starting with $0$. In base $10$, the $i=2$ digit is the hundreds digit (because we started counting with zero), and the value is $10^2$
$endgroup$
– Ross Millikan
Nov 21 '13 at 14:17
add a comment |
$begingroup$
So what's i in this?
$endgroup$
– Kasun Jayasuriya
Nov 21 '13 at 14:10
$begingroup$
It is the number of the digit, counting from the right and starting with $0$. In base $10$, the $i=2$ digit is the hundreds digit (because we started counting with zero), and the value is $10^2$
$endgroup$
– Ross Millikan
Nov 21 '13 at 14:17
$begingroup$
So what's i in this?
$endgroup$
– Kasun Jayasuriya
Nov 21 '13 at 14:10
$begingroup$
So what's i in this?
$endgroup$
– Kasun Jayasuriya
Nov 21 '13 at 14:10
$begingroup$
It is the number of the digit, counting from the right and starting with $0$. In base $10$, the $i=2$ digit is the hundreds digit (because we started counting with zero), and the value is $10^2$
$endgroup$
– Ross Millikan
Nov 21 '13 at 14:17
$begingroup$
It is the number of the digit, counting from the right and starting with $0$. In base $10$, the $i=2$ digit is the hundreds digit (because we started counting with zero), and the value is $10^2$
$endgroup$
– Ross Millikan
Nov 21 '13 at 14:17
add a comment |
$begingroup$
In base 16, each number is composed of a series of the digits 0-9 and A-F, where, A represents 10, B 11, C 12 and so on up to the maximum for any digit which is F, representing 15.
As such, AB$3$ represents $10$ in the $16^2=256$s column, $11$ in the $16^1=16$s column and 3 in the units column, so in decimal (base 10) that's $10(256)+11(16)+3=2739$.
In general, for a natural number $n$, given a number in base $n$, the digit at the far right tells you how many units, the digit to the left of that how many $n$s, the next digit to the left how many $n^2$s etc. None of the digits in a number in base $n$ is allowed to exceed $n-1$.
For how to convert the number to base 2, see the algorithm presented in Adi Dani's answer.
$endgroup$
add a comment |
$begingroup$
In base 16, each number is composed of a series of the digits 0-9 and A-F, where, A represents 10, B 11, C 12 and so on up to the maximum for any digit which is F, representing 15.
As such, AB$3$ represents $10$ in the $16^2=256$s column, $11$ in the $16^1=16$s column and 3 in the units column, so in decimal (base 10) that's $10(256)+11(16)+3=2739$.
In general, for a natural number $n$, given a number in base $n$, the digit at the far right tells you how many units, the digit to the left of that how many $n$s, the next digit to the left how many $n^2$s etc. None of the digits in a number in base $n$ is allowed to exceed $n-1$.
For how to convert the number to base 2, see the algorithm presented in Adi Dani's answer.
$endgroup$
add a comment |
$begingroup$
In base 16, each number is composed of a series of the digits 0-9 and A-F, where, A represents 10, B 11, C 12 and so on up to the maximum for any digit which is F, representing 15.
As such, AB$3$ represents $10$ in the $16^2=256$s column, $11$ in the $16^1=16$s column and 3 in the units column, so in decimal (base 10) that's $10(256)+11(16)+3=2739$.
In general, for a natural number $n$, given a number in base $n$, the digit at the far right tells you how many units, the digit to the left of that how many $n$s, the next digit to the left how many $n^2$s etc. None of the digits in a number in base $n$ is allowed to exceed $n-1$.
For how to convert the number to base 2, see the algorithm presented in Adi Dani's answer.
$endgroup$
In base 16, each number is composed of a series of the digits 0-9 and A-F, where, A represents 10, B 11, C 12 and so on up to the maximum for any digit which is F, representing 15.
As such, AB$3$ represents $10$ in the $16^2=256$s column, $11$ in the $16^1=16$s column and 3 in the units column, so in decimal (base 10) that's $10(256)+11(16)+3=2739$.
In general, for a natural number $n$, given a number in base $n$, the digit at the far right tells you how many units, the digit to the left of that how many $n$s, the next digit to the left how many $n^2$s etc. None of the digits in a number in base $n$ is allowed to exceed $n-1$.
For how to convert the number to base 2, see the algorithm presented in Adi Dani's answer.
edited Nov 26 '13 at 19:06
answered Nov 21 '13 at 14:11
George TomlinsonGeorge Tomlinson
1,216711
1,216711
add a comment |
add a comment |
$begingroup$
$$n=(AB3)_{16}=Acdot16^2+Bcdot 16^1+3cdot 16^0=10cdot256+11cdot16+3cdot1=2739$$
$$2739:2=1369+1$$
$$1369:2=2cdot684+1$$
$$684:2=2cdot342+0$$
$$342:2=2cdot171+0$$
$$171:2=2cdot85+1$$
$$85:2=2cdot42+1$$
$$42:2=2cdot21+0$$
$$21:2=2cdot10+1$$
$$10:2=2cdot5+0$$
$$5:2=2cdot2+1$$
$$2=2cdot1+0$$
$$2739=(101010110011)_2$$
$endgroup$
$begingroup$
I gave you +1 without having checked your base 2 assertion, which is incorrect, but the algorithm is useful, so you deserve the +1. 110011001111 is not 2739 in base 2: it's 3279. $$110011001111=2048+1024+128+64+8+4+2+1=3279$$ The error is in the second line (and hence, as you know, all subsequent lines are inapplicable too), which should be $$1639=684⋅2+1$$
$endgroup$
– George Tomlinson
Nov 22 '13 at 20:43
1
$begingroup$
I edit my answer now is correct. I use $1639$ instead of $1369$ Thank you @bluesh34
$endgroup$
– Adi Dani
Nov 22 '13 at 22:34
$begingroup$
No problems. Oh, yeah: I meant 1369.
$endgroup$
– George Tomlinson
Nov 25 '13 at 17:54
add a comment |
$begingroup$
$$n=(AB3)_{16}=Acdot16^2+Bcdot 16^1+3cdot 16^0=10cdot256+11cdot16+3cdot1=2739$$
$$2739:2=1369+1$$
$$1369:2=2cdot684+1$$
$$684:2=2cdot342+0$$
$$342:2=2cdot171+0$$
$$171:2=2cdot85+1$$
$$85:2=2cdot42+1$$
$$42:2=2cdot21+0$$
$$21:2=2cdot10+1$$
$$10:2=2cdot5+0$$
$$5:2=2cdot2+1$$
$$2=2cdot1+0$$
$$2739=(101010110011)_2$$
$endgroup$
$begingroup$
I gave you +1 without having checked your base 2 assertion, which is incorrect, but the algorithm is useful, so you deserve the +1. 110011001111 is not 2739 in base 2: it's 3279. $$110011001111=2048+1024+128+64+8+4+2+1=3279$$ The error is in the second line (and hence, as you know, all subsequent lines are inapplicable too), which should be $$1639=684⋅2+1$$
$endgroup$
– George Tomlinson
Nov 22 '13 at 20:43
1
$begingroup$
I edit my answer now is correct. I use $1639$ instead of $1369$ Thank you @bluesh34
$endgroup$
– Adi Dani
Nov 22 '13 at 22:34
$begingroup$
No problems. Oh, yeah: I meant 1369.
$endgroup$
– George Tomlinson
Nov 25 '13 at 17:54
add a comment |
$begingroup$
$$n=(AB3)_{16}=Acdot16^2+Bcdot 16^1+3cdot 16^0=10cdot256+11cdot16+3cdot1=2739$$
$$2739:2=1369+1$$
$$1369:2=2cdot684+1$$
$$684:2=2cdot342+0$$
$$342:2=2cdot171+0$$
$$171:2=2cdot85+1$$
$$85:2=2cdot42+1$$
$$42:2=2cdot21+0$$
$$21:2=2cdot10+1$$
$$10:2=2cdot5+0$$
$$5:2=2cdot2+1$$
$$2=2cdot1+0$$
$$2739=(101010110011)_2$$
$endgroup$
$$n=(AB3)_{16}=Acdot16^2+Bcdot 16^1+3cdot 16^0=10cdot256+11cdot16+3cdot1=2739$$
$$2739:2=1369+1$$
$$1369:2=2cdot684+1$$
$$684:2=2cdot342+0$$
$$342:2=2cdot171+0$$
$$171:2=2cdot85+1$$
$$85:2=2cdot42+1$$
$$42:2=2cdot21+0$$
$$21:2=2cdot10+1$$
$$10:2=2cdot5+0$$
$$5:2=2cdot2+1$$
$$2=2cdot1+0$$
$$2739=(101010110011)_2$$
edited Nov 22 '13 at 22:30
answered Nov 21 '13 at 14:12
Adi DaniAdi Dani
15.3k32246
15.3k32246
$begingroup$
I gave you +1 without having checked your base 2 assertion, which is incorrect, but the algorithm is useful, so you deserve the +1. 110011001111 is not 2739 in base 2: it's 3279. $$110011001111=2048+1024+128+64+8+4+2+1=3279$$ The error is in the second line (and hence, as you know, all subsequent lines are inapplicable too), which should be $$1639=684⋅2+1$$
$endgroup$
– George Tomlinson
Nov 22 '13 at 20:43
1
$begingroup$
I edit my answer now is correct. I use $1639$ instead of $1369$ Thank you @bluesh34
$endgroup$
– Adi Dani
Nov 22 '13 at 22:34
$begingroup$
No problems. Oh, yeah: I meant 1369.
$endgroup$
– George Tomlinson
Nov 25 '13 at 17:54
add a comment |
$begingroup$
I gave you +1 without having checked your base 2 assertion, which is incorrect, but the algorithm is useful, so you deserve the +1. 110011001111 is not 2739 in base 2: it's 3279. $$110011001111=2048+1024+128+64+8+4+2+1=3279$$ The error is in the second line (and hence, as you know, all subsequent lines are inapplicable too), which should be $$1639=684⋅2+1$$
$endgroup$
– George Tomlinson
Nov 22 '13 at 20:43
1
$begingroup$
I edit my answer now is correct. I use $1639$ instead of $1369$ Thank you @bluesh34
$endgroup$
– Adi Dani
Nov 22 '13 at 22:34
$begingroup$
No problems. Oh, yeah: I meant 1369.
$endgroup$
– George Tomlinson
Nov 25 '13 at 17:54
$begingroup$
I gave you +1 without having checked your base 2 assertion, which is incorrect, but the algorithm is useful, so you deserve the +1. 110011001111 is not 2739 in base 2: it's 3279. $$110011001111=2048+1024+128+64+8+4+2+1=3279$$ The error is in the second line (and hence, as you know, all subsequent lines are inapplicable too), which should be $$1639=684⋅2+1$$
$endgroup$
– George Tomlinson
Nov 22 '13 at 20:43
$begingroup$
I gave you +1 without having checked your base 2 assertion, which is incorrect, but the algorithm is useful, so you deserve the +1. 110011001111 is not 2739 in base 2: it's 3279. $$110011001111=2048+1024+128+64+8+4+2+1=3279$$ The error is in the second line (and hence, as you know, all subsequent lines are inapplicable too), which should be $$1639=684⋅2+1$$
$endgroup$
– George Tomlinson
Nov 22 '13 at 20:43
1
1
$begingroup$
I edit my answer now is correct. I use $1639$ instead of $1369$ Thank you @bluesh34
$endgroup$
– Adi Dani
Nov 22 '13 at 22:34
$begingroup$
I edit my answer now is correct. I use $1639$ instead of $1369$ Thank you @bluesh34
$endgroup$
– Adi Dani
Nov 22 '13 at 22:34
$begingroup$
No problems. Oh, yeah: I meant 1369.
$endgroup$
– George Tomlinson
Nov 25 '13 at 17:54
$begingroup$
No problems. Oh, yeah: I meant 1369.
$endgroup$
– George Tomlinson
Nov 25 '13 at 17:54
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f575971%2fconverting-base-16-digits-to-base-2-and-10-analysis-question%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
If you understand radix notation (binary, hexadecimal, decimal) then the Question is rather straightforward. You are being given the hexadecimal presentation of a number, and asked re-present the same number as binary and decimal expressions.
$endgroup$
– hardmath
Nov 21 '13 at 14:03