Binary operations and proofs
$begingroup$
Let $text{binary}(a)$ denote the binary representation of a base-$10$ number $a$. Are the following statements correct? If yes, where can I find the proofs?
(1) $text{binary}(atimes b)=text{binary}(a)times text{binary}(b)$
(2) $text{binary}(a+b)=text{binary}(a)+text{binary}(b)$
(3) $text{binary}(atimes (b+c))=text{binary}(atimes
> b)+text{binary}(atimes c)$
binary binary-operations
edited Dec 12 '18 at 10:01
Klangen
1,69811334
asked Sep 26 '15 at 13:22
MengMeng
1212
$endgroup$
add a comment |
$begingroup$
Let $text{binary}(a)$ denote the binary representation of a base-$10$ number $a$. Are the following statements correct? If yes, where can I find the proofs?
(1) $text{binary}(atimes b)=text{binary}(a)times text{binary}(b)$
(2) $text{binary}(a+b)=text{binary}(a)+text{binary}(b)$
(3) $text{binary}(atimes (b+c))=text{binary}(atimes
> b)+text{binary}(atimes c)$
binary binary-operations
edited Dec 12 '18 at 10:01
Klangen
1,69811334
asked Sep 26 '15 at 13:22
MengMeng
1212
$endgroup$
1
$begingroup$
How do you define * ?
$endgroup$
– Shailesh
Sep 26 '15 at 13:26
1
$begingroup$
So, your question is about why do decimal fractions satisfy the field axioms, am I right?
$endgroup$
– Michael Freimann
Dec 31 '16 at 11:49
add a comment |
$begingroup$
Let $text{binary}(a)$ denote the binary representation of a base-$10$ number $a$. Are the following statements correct? If yes, where can I find the proofs?
(1) $text{binary}(atimes b)=text{binary}(a)times text{binary}(b)$
(2) $text{binary}(a+b)=text{binary}(a)+text{binary}(b)$
(3) $text{binary}(atimes (b+c))=text{binary}(atimes
> b)+text{binary}(atimes c)$
binary binary-operations
edited Dec 12 '18 at 10:01
Klangen
1,69811334
asked Sep 26 '15 at 13:22
MengMeng
1212
$endgroup$
Let $text{binary}(a)$ denote the binary representation of a base-$10$ number $a$. Are the following statements correct? If yes, where can I find the proofs?
(1) $text{binary}(atimes b)=text{binary}(a)times text{binary}(b)$
(2) $text{binary}(a+b)=text{binary}(a)+text{binary}(b)$
(3) $text{binary}(atimes (b+c))=text{binary}(atimes
> b)+text{binary}(atimes c)$
binary binary-operations
binary binary-operations
edited Dec 12 '18 at 10:01
Klangen
1,69811334
asked Sep 26 '15 at 13:22
MengMeng
1212
edited Dec 12 '18 at 10:01
Klangen
1,69811334
asked Sep 26 '15 at 13:22
MengMeng
1212
edited Dec 12 '18 at 10:01
Klangen
1,69811334
edited Dec 12 '18 at 10:01
Klangen
1,69811334
edited Dec 12 '18 at 10:01
Klangen
1,69811334
1,69811334
asked Sep 26 '15 at 13:22
MengMeng
1212
asked Sep 26 '15 at 13:22
MengMeng
1212
asked Sep 26 '15 at 13:22
MengMeng
1212
1212
1
$begingroup$
How do you define * ?
$endgroup$
– Shailesh
Sep 26 '15 at 13:26
1
$begingroup$
So, your question is about why do decimal fractions satisfy the field axioms, am I right?
$endgroup$
– Michael Freimann
Dec 31 '16 at 11:49
add a comment |
1
$begingroup$
How do you define * ?
$endgroup$
– Shailesh
Sep 26 '15 at 13:26
1
$begingroup$
So, your question is about why do decimal fractions satisfy the field axioms, am I right?
$endgroup$
– Michael Freimann
Dec 31 '16 at 11:49
1
1
$begingroup$
How do you define * ?
$endgroup$
– Shailesh
Sep 26 '15 at 13:26
$begingroup$
How do you define * ?
$endgroup$
– Shailesh
Sep 26 '15 at 13:26
1
1
$begingroup$
So, your question is about why do decimal fractions satisfy the field axioms, am I right?
$endgroup$
– Michael Freimann
Dec 31 '16 at 11:49
$begingroup$
So, your question is about why do decimal fractions satisfy the field axioms, am I right?
$endgroup$
– Michael Freimann
Dec 31 '16 at 11:49
add a comment |
0
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1
$begingroup$
How do you define * ?
$endgroup$
– Shailesh
Sep 26 '15 at 13:26
1
$begingroup$
So, your question is about why do decimal fractions satisfy the field axioms, am I right?
$endgroup$
– Michael Freimann
Dec 31 '16 at 11:49