Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sorry for my math language and the question header; I'm not capable of the terms used for the mathematics to ask the question via text; so I had to use the example above; feel free to edit if you can keep the meaning the same.

So the question is like this: I know that the total is uniquely identifies the used exponential constants while using the base as $2$; like $2^x + 2^y = 129$ then the $x=0$ and $y=7$.

So I couldn't think of a function to get the values like $\operatorname{func}(129) = [0,7]$.

Thanks in advance. Note: I know it's dumb to ask that but help is appreciated.

share|improve this question
actually $x=0$ ($129=1+128$) –  Andrea Mori Mar 27 '12 at 13:54
@AndreaMori sorry for that(: –  Beytan Kurt Mar 27 '12 at 13:55

4 Answers 4

up vote 1 down vote accepted

The function you are looking for is called dec2bin, when you are using Matlab. It would convert $129_{10}$ in decimal to $10000001_2$ in binary notation. As dec2base it works for other bases as well.

share|improve this answer
Thanks for that, I should have thought binary way while all the problem is base 2; thanks(: –  Beytan Kurt Mar 27 '12 at 14:05
I would also like to mention Windows calculator has a programmer mode. Simply input the number as a decimal number and it will show you the binary representation with spaces every 4 bits to make counting easier. –  Mike Mar 27 '12 at 17:31
Thanks but I'll use it for programming, so no calculator included. –  Beytan Kurt Mar 27 '12 at 19:03

If $x>0 ~\text{and}~y>0 $ then $2^x+2^y$ is an even number . Hence :


share|improve this answer
I couldn't understand how you could find the result?? there's no tip to find 0 or 7?? –  Beytan Kurt Mar 27 '12 at 14:01
$2^x+2^y $ can be odd number only if $x=0 ~\text{or}~ y=0$ , therefore it is easy to calculate that value of the second variable has to be $7$ . –  pedja Mar 27 '12 at 14:08
I've asked for a function or a method to evaluate; your answer gives the how easy it is explanation; not the method but thanks. –  Beytan Kurt Mar 27 '12 at 14:33

I'm not sure what is actually the question, but the problem of writing a number $n\in\Bbb N$ as a sum of powers of $2$ is equivalent to finding its expression in base $2$.

share|improve this answer
I don't think that 2^x + 2^y = 2^(x+y); the question is a workaround to keep a single number that could give multiple selection numbers like categoryA=0, categoryB=1, categoryZ=7 then when a result is given like 129 I can uniquely identify that catA and catZ is used with a single result –  Beytan Kurt Mar 27 '12 at 14:01
As I told you, it is equivalent to find the expansion of n in base 2 and this is obtained by a repeated division by 2 keeping track of the remainders. For instance $129=2\cdot64+1$, $64=2\cdot32+0$, $32=2\cdot16+0$, $16=2\cdot8+0$, $8=2\cdot4+0$, $4=2\cdot2+0$, $2=2\cdot1+0$ and $1=2\cdot0+1$. Thus, $129=10000001$ (binary), i.e. $129=2^0+2^7$ because you have $1$ only in the $0$-th and $7$-th place. –  Andrea Mori Mar 27 '12 at 16:02
Thanks a lot (: –  Beytan Kurt Mar 27 '12 at 19:01

Hint $\ $ For naturals $\rm\:b>1,\ x < y,\:$ if $\rm\: n\: =\: b^{x} + b^{y} =\: b^x\: (1 + b^{y-x})\:$ then $\rm\:x\:$ is determined uniquely as the greatest power of $\rm\:b\:$ that divides $\rm\:n,\:$ and $\rm\:y\:$ is determined uniquely as $\rm\:x\:$ plus the greatest power of $\rm\:b\:$ that divides $\rm\:n/b^{x}-1.$

This is a special case of the existence and uniqueness of radix representation, which follows from that for the division algorithm (here repeated division by the radix $\rm b$).

share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.