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Write a program that checks if the integer is a power of 2.

Sample input:


Sample output:


Sample input:


Sample output:



  • Don't use +,- operations.

  • Use some sort of input stream to get the number (it is supposed to be typed). Input is not supposed to be initially stored in a variable.

  • The shortest code (in bytes) wins.

P.S. You can use any positive/negative response (for instance, true/false). You may assume that input number is greater than 0.

Thanks to you, guys, this question became very popular and got a bunch of different answers with interesting approaches, so I decided to append some info to make this thread readable. Code Golf is not only programming languages battle, it is also a challenge for different approaches within a single language. I decided to sum up interim results and note the leaders for every programming language for better navigation within the thread.

GTB - 17 characters - Timtech

GolfScript - 6 characters - Ilmari Karonen

PHP - 58 - 58 characters - Joachim Isaksson

JavaScript - 35 characters - copy

Python - 31 characters - boothby

Perl 6 - 17 characters - xfix

Perl 5 - 14 characters - Ilmari Karonen

Octave - 23 characters - Joachim Isaksson

APL - 7 characters - marinus

R - 11 characters - Sven Hohenstein

Mathematica - 21 characters - ybeltukov

K - 24 characters - Kyle Kanos

Ruby - 19 characters - O-I

Scheme - 40 characters - Sylwester

C - 48 characters - nightcracker

Haskell - 50 - Zeta

J - 14 characters - FireFly

D - 83 characters - rachet freak

C# - 58 characters - Merin Nakarmi

AutoHotkey - 45 characters - user13542

This table will be updated with new answers posted.

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Is it also allowed to output "true" instead of "yes" and "false" instead of "no"? –  ProgramFOX Jan 4 at 14:38
Yes, you can use any positive/negative response. Question is updated. –  gthacoder Jan 4 at 14:42
The pred function, when applied to an integer n, returns n - 1. Are functions such as this, which are thin disguises around the forbidden operator, also forbidden? –  Wayne Conrad Jan 4 at 15:35
@Wayne just like golfscript's ), or most c-based languages' --. –  Doorknob 冰 Jan 4 at 15:38
Can we output 1 or 0? 'T' or 'F'? –  Mark Plotnick Jan 4 at 15:43

59 Answers 59

up vote 7 down vote accepted

GolfScript, 6 chars, no decrements


Here's a solution that doesn't use the x & (x-1) method in any form. It uses x & (x/3) instead. ;-) Outputs 0 if false, 1 if true.


  • ~ evals the input string to turn it into a number,
  • . duplicates it (for the subsequent &),
  • 3/ divides it by three (truncating down),
  • & computes the bitwise AND of the divided value with the original, which will be zero if and only if the input is zero or a power of two (i.e. has at most one bit set), and
  • ! logically negates this, mapping zero to one and all other values to zero.


  • Per the clarified rules, zero is not a valid input, so this code is OK, even though it outputs 1 if the input is zero.

  • If the GolfScript decrement operator ( is allowed, then the 5-character solution ~.(&! posted by aditsu is enough. However, it seems to go against the spirit of the rules, if not the letter.

  • I came up with the x & (x/3) trick years ago on the Fun With Perl mailing list. (I'm sure I'm not the first to discover it, but I did (re)invent it independently.) Here's a link to the original post, including a proof that it actually works.

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I think it is a bit silly really, golfscript allows one to write the exact solution that the OP wanted to exclude without actually breaking the rules. –  Tim Seguine Jan 4 at 22:56
@Tim: OK, here's one without decrements, then. ;) –  Ilmari Karonen Jan 4 at 23:05
how can this work? For example 7/3 = 2 (0010), so 7 & 2 = 0111 & 0010 = 0010 which clearly the last bit is not 1 –  Lưu Vĩnh Phúc Jan 5 at 2:06
@LưuVĩnhPhúc: No, but the second bit is. Try doing long division by 3 in binary and it's pretty obvious why this always happens if the dividend has more than one bit set. –  Ilmari Karonen Jan 5 at 2:08
ah I misread this with "divisible by 2" –  Lưu Vĩnh Phúc Jan 5 at 2:25

APL (7)

Yes, that's 7 bytes. Assume for the moment that I'm using IBM codepage 907 instead of Unicode and then each character is a byte :)


i.e. 0 = mod(log(input(),2),1)

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Just wondering, what happens if you give it 0 or a negative number? –  aditsu Jan 4 at 21:34
@aditsu I don´t know what infinity mod 1 is, but it certainly shouldn't be zero. –  Tim Seguine Jan 4 at 22:45

GolfScript, 11 (for 1 (true) and 0 (false))


Put the number on the stack and then run.

GolfScript, 22 (for Yes/No)


I love how converting 1/0 to Yes/No takes as much code as the challenge itself :D

Warning: EXTREMELY inefficient ;) It does work fine for numbers up to 10000, but once you get that high you start to notice slight lag.


  • .,: turns n into n 0..n (. duplicate, , 0..n range)
  • {2\?}: to the power of 2
  • %: map "power of 2" over "0..n" so it becomes n [1 2 4 8 16 ...]
  • ?0>: checks to see if the array contains the number (0 is greater than index)
share|improve this answer
1 byte shorter for Yes/No: .,{2\?}%?0<'YesNo'3/=; also I think you're cheating by asking to "Put the number on the stack", you should start with a ~. –  aditsu Jan 4 at 16:04
Fails on 1, which is 2^0 –  Joachim Isaksson Jan 4 at 21:01

Mathematica 28


For integer powers of 2, the numerator of the base 2 log will be 1 (meaning that the log is a unit fraction).

Here we modify the function slightly to display the presumed input. We use # in place of Input[] and add & to define a pure function. It returns the same answer that would be returned if the user input the number in the above function.

    Numerator[#~Log~2] == 1 &[1024]
    Numerator[#~Log~2] == 1 &[17]


Testing several numbers at a time.

    Numerator[#~Log~2] == 1 &&/@{64,8,7,0}

{True, True, False, False}

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Octave (15 23)

EDIT: Updated due to user input requirement;


Lets the user input a value and outputs 1 for true, 0 for false.

Tested in Octave, should work in Matlab also.

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Works in Matlab also :) –  Jubobs Jan 5 at 1:01

R, 13 11

Based on the Perl solution. Returns FALSE or TRUE.


The parameter i represents the input variable.

An alternative version with user input:

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GolfScript, 5

Outputs 1 for true, 0 for false. Based on user3142747's idea:


Note: ( is decrement, hopefully it doesn't count as - :)
If it does (and the OP's comments suggest that it might), then please refer to Ilmari Karonen's solution instead.
For Y/N output, append 'NY'1/= at the end (7 more bytes).

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Perl 6 (17 characters)

say get.log(2)%%1

This program gets a line from STDIN get function, calculates logarithm with base 2 on it (log(2)), and checks if the result divides by 1 (%%1, where %% is divides by operator). Not as short as GolfScript solution, but I find this acceptable (GolfScript wins everything anyway), but way faster (even considering that Perl 6 is slow right now).

~ $ perl6 -e 'say get.log(2)%%1'
~ $ perl6 -e 'say get.log(2)%%1'
share|improve this answer
The reason that + and - are forbidden for this challenge, is because if x & (x - 1) is equal to 0, then x is a power of 2. –  ProgramFOX Jan 4 at 15:21
@ProgramFOX: I see. Interesting trick. –  xfix Jan 4 at 15:27
@ProgramFOX But x&~(~0*x) still works. That's only 2 characters longer. –  orlp Jan 5 at 12:24

Python, 31

print 3>bin(input()).rfind('1')
share|improve this answer
31 if you do bin(input()).rfind('1')<3 –  Blender Jan 4 at 21:44
@Blender Well-spotted. I'd used 2== because I figured it should work for nonpositive numbers too. That's explicitly not required by the rules, so... –  boothby Jan 4 at 23:39
+1. I was going to post print bin(input()).count('1')<2 at a total of 31 characters, but it's too similar to yours. –  Steven Rumbalski Jan 7 at 17:39

I decided to to use another approach, based on the population count or sideways sum of the number (the number of 1-bits). The idea is that all powers of two have exactly one 1 bit, and no other number does. I added a JavaScript version because I found it hilarious, though it certainly won't win any golfing competition.

J, 14 chars (outputs 0 or 1)


JavaScript, 76 chars (outputs true or false)

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JavaScript, 41 40 characters


How this works: you take the logarithm at base 2 using l(prompt()) / l(2), and if that result modulo 1 is equal to zero, then it is a power of 2.

For example: after taking the logarithm of 8 on base 2, you get 3. 3 modulo 1 is equal to 0, so this returns true.

After taking the logarithm of 7 on base 2, you get 2.807354922057604. 2.807354922057604 modulo 1 is equal to 0.807354922057604, so this returns false.

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You don't need to cast the input to a number; Math.log will do that already: "Each of the following Math object functions applies the ToNumber abstract operator to each of its arguments..." –  apsillers Jan 4 at 15:36
@apsillers: Thanks! –  ProgramFOX Jan 4 at 15:48
Doesn't it suffer from numerical inaccuracies? –  Mark Jeronimus Apr 11 at 6:42
@MarkJeronimus: I actually don't know. It could be, but I haven't yet encountered an incorrect result. –  ProgramFOX Apr 11 at 8:41

Javascript (37)


Simple script that just divides by 2 repeatedly and checks the remainder.

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same idea with a for loop (also 37 chars) for(i=prompt();i>1;i/=2){}alert(i==1) –  tryingToGetProgrammingStraight Jan 5 at 6:17

JavaScript, 35

Works for bytes.


46 character version, Works for 16 bit numbers.


The trick works in most dynamic languages.

Explanation: Convert the number to base 2, interpret that string as base 10, do modulo 9 to get the digit sum, which must be 1.

share|improve this answer
What about 0x2ff, which in base 2 is 1111111111? –  Peter Taylor Jan 4 at 18:52
@PeterTaylor You're right, fixed –  copy Jan 4 at 19:19
so the real thing your doing is checking for modulo 10 without a remainder, but you used 9 to shave a character of your code, +1! –  tryingToGetProgrammingStraight Jan 5 at 6:09

Mathematica (21)


Without input it is a bit shorter





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⌊#⌋==#&@Log2@Input[] –  alephalpha Jan 5 at 5:53

Perl 5.10+, 13 + 1 = 14 chars


Uses the same method from an old FWP thread as my GolfScript entry. Prints 1 if the input is a power of two, and an empty line otherwise.

Needs to be run with perl -nE; the n costs one extra char, for a total of 14 chars. Alternatively, here's an 18-character version that doesn't need the n:

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python 3, 38


python, 32

However, the code doesn't work in every version.

print 1==bin(input()).count('1')

Notice that the solution works also for 0 (print False).

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Upvoted because this was my solution as well. –  Josh Caswell Jan 4 at 22:02
What if you replace == with &? –  SimonT Jan 4 at 22:09
@SimonT This is not true. Replacing the '==' with '&' will print 1 for every number that has odd number of '1' in its binary representation. Check for example 7=111. There are 3=11 ones. It will return 11&1 = 1. –  Gari BN Jan 5 at 8:37

C, 48

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Can be shorter if unary negate is allowed, is longer if negative constants aren't allowed. Assumes two's complement. –  orlp Jan 4 at 21:26
* has higher precedence than binary &, you don't need the parens. And if return value is accepted (just asked) exit(x&x*-1) would be much shorter. –  Kevin Jan 4 at 23:36
There is a -: x*-1. –  klingt.net Jan 5 at 0:24
@klingt.net yes, but that's part of a numerical constant. Technically, as it is worded now, only the operator - is forbidden. –  Kevin Jan 5 at 3:14
@klingt.net Replaced it with a version that uses no signs. –  orlp Jan 5 at 11:18

Ruby — 17 characters (fourth try)

p /.1/!~'%b'%gets

My current best is a fusion of @steenslag's answer with my own. Below are my previous attempts.

Ruby — 19 characters (third try)

p /10*1/!~'%b'%gets

Ruby — 22 characters (second try)

p !('%b'%gets)[/10*1/]

Ruby — 24 characters (first try)

p !!('%b'%gets=~/^10*$/)
share|improve this answer
there's still a "+" in your program –  Lưu Vĩnh Phúc Jan 5 at 1:21
I know. :-/ I've asked for clarification whether '+' and '-' are strictly forbidden, or whether they can be used in other contexts besides addition and subtraction. I'm in the process of rewriting regardless. –  O-I Jan 5 at 1:27
Great improvement. It seems like it's the best Ruby result so far. I updated the leaders table in the question text. –  gthacoder Jan 5 at 22:24
@gthacoder Just combined steenslag's regex with my binary formatting. Definitely can't take all the credit. –  O-I Jan 5 at 22:28

K/Kona (24 17)

d:{(+/(2_vs x))~1

Returns 1 if true and 0 if false. Any power of 2 has a single bit equal to 1:

1 0
1 0 0
1 0 0 0
1 0 0 0 0
1 0 0 0 0 0
1 0 0 0 0 0 0
1 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0)

(this prints out all the powers of 2 (from 0 to 9) in binary)

So I sum up all the components of the binary expression of x and see if it's equal to 1; if yes then x=2^n, otherwise nope.

...knew I could make it smaller

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@gthacoder: I made the code smaller, hope you can update you main post to reflect this! –  Kyle Kanos Jan 6 at 2:57

C# (54 characters)

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The task clearly states that input is not stored in a variable, it should be obtained from an input stream of some kind (like stdin), also, this is code-golf, try shortening your code a little, at least by removing whitespace –  mniip Jan 5 at 5:09
Thanks mniip, I edited it to meet the requirement. –  Merin Nakarmi Jan 5 at 5:36
I think you just mean Int32, not ToInt32... –  Chris Jan 5 at 22:56
Ya ya. Thanks for pointing out Chris. Earlier it was Convert.ToInt32 and I wanted to change it to Int32.Parse to shorten it. :D –  Merin Nakarmi Jan 6 at 1:50
use int instead of Int32 for 2 fewer characters. –  Rik Jan 7 at 11:25

Rebmu (9 chars)

z?MOl2A 1


>> rebmu/args [z?MOl2A 1] 7
== false

>> rebmu/args [z?MOl2A 1] 8 
== true

>> rebmu/args [z?MOl2A 1] 9 
== false

Rebmu is a constricted dialect of Rebol. The code is essentially:

z? mo l2 a 1  ; zero? mod log-2 input 1


14 chars—Rebmu does not have a 'mushed' bitwise AND~

z?AND~aTIddA 3

In Rebol:

zero? a & to-integer a / 3
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GTB, 46 bytes

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Python, 35

print bin(input()).strip('0')=='b1'

Doesn't use not only +/- operations, but any math operations aside from converting to binary form.

Other stuff (interesting, but not for competition):

I have also a regexp version (61):

import re;print re.match(r'^0b10+$',bin(input())) is not None

(Love the idea, but import and match function make it too long)

And nice, but boring bitwise operations version (31):

x=input();print x and not x&~-x

(yes, it's shorter, but it uses ~-x for decrement which comtains - operation)

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boothby's answers uses the same idea as my first, but is shorter :( –  Ivan Anishchuk Jan 4 at 18:02

Python 2.7 (30 29 39 37)

EDIT: Updated due to user input requirement;

while a>1:a/=2.
print a==1

Brute force, try to divide until =1 (success) or <1 (fail)

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not a%2 can be written as a%2==0. Granted, this would be longer in many languages, but not Python. –  xfix Jan 4 at 15:11
@xfix Thanks, tested and updated. –  Joachim Isaksson Jan 4 at 15:12
or even better, a%2<1. –  boothby Jan 4 at 17:18

Python (33)

print int(bin(input())[3:]or 0)<1
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int(bin(input()*2)[3:])<1 also works from the python shell with only 25 chars. –  gmatht Apr 6 at 23:28

Ruby, 33, 28, 25

p /.1/!~gets.to_i.to_s(2)
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APL (12 for 0/1, 27 for yes/no)


or, if we must output text:

3↑(3x≠/A=2*0,ιA←⍞)↓'YESNO '

Read in A. Form a vector 0..A, then a vector 20..2A (yes, that's way more than necessary), then a vector comparing A with each of those (resulting in a vector of 0's and at most one 1), then xor that (there's no xor operator in APL, but ≠ applied to booleans will act as one.) We now have 0 or 1.

To get YES or NO: multiply the 0 or 1 by 3, drop this number of characters from 'YESNO ', then take the first 3 characters of this.

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C, 65 bytes

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You can cut off 5 chars by using main(k){..., relying on the implicit int typing. It might be UB, but this is code golf. NEVER use something like that in production, of course. –  Kevin Jan 5 at 0:22

Bash + dc + grep, 24

dc -e2o?p|grep -c ^10\*$

Reads from stdin. Outputs "1" if a power of 2 and "0" otherwise:

$ dc -e2o?p|grep -c ^10\*$
$ dc -e2o?p|grep -c ^10\*$

Pure Bash (only builtins), 40

[[ `read a;printf %o $a` =~ ^[124]0*$ ]]

Reads from stdin. Returns success (0) if a power of 2 and failure (1) otherwise:

$ [[ `read a;printf %o $a` =~ ^[124]0*$ ]]
$ echo $?
$ [[ `read a;printf %o $a` =~ ^[124]0*$ ]]
$ echo $?
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PHP, 86 chars

function P($a,$c){if($c==$a)return 1;if($c>$a)return 0;return P($a,$c*2);}echo P(x,2);

Replace x with the number you want to test.

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I'm almost sure this can be shorter, by use of ternary operator... then again, ternary operator in PHP is rather strange, so you may need some parenthesis to enforce precedence. –  xfix Jan 4 at 15:36

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