# Convert from base 10 to base 2 without built-in base conversions

Background:

You have been given an assignment to convert base 10 numbers to base 2 without using any premade base conversion functions. You can't use any imported libraries either.

Problem:

Convert an input string from base 10 (decimal) to base 2 (binary). You may not use any premade base conversion code/functions/methods, or imported libraries. Since this is , the shortest answer in bytes will win.

Input will be anything from -32768 to 32767 (include sign byte handling in your code)

• Q: what does "sign byte handling" mean - shall I output "-xxxx" for a negative number? Then some of us are wrong, incl. me, as I output "11...11" for -1 (aka as unsigned) Feb 16, 2014 at 2:19
• Sign byte handling - the MSB of signed variables controls if they are negative Feb 16, 2014 at 3:12
• sure, but do I have to >print< them as sign '-' followed by magnitude? Feb 16, 2014 at 3:14
• @blabla999 - No you don't Feb 16, 2014 at 3:34
• the MSB of signed variables controls if they are negative - that sounds like sign bit, however as the range -32768..32767 suggests, you want 2's complement. So which do you want?.. Feb 16, 2014 at 12:03

# JavaScript, 46

for(x=prompt(o='');x;x>>>=1)o=(x&1)+o;alert(o)

• Lol, I didn't even know that a 4-character operator (>>>=) existed! +1 (Also, if you run it in the console, you can save the last 9 characters.) Feb 16, 2014 at 3:53
• It's not 4-characters, it's two operators: the >>> is the 0-filling bitwise right shift, followed by an assignment. Try: x=8; x>>>=1; x; and x=8; x>>>1; x; -- in the first case, the value of x has changed; in the second, it has not. Feb 16, 2014 at 9:03
• @GrahamCharles >>>= is a single operator. Feb 16, 2014 at 13:43
• Well, look at that! Thanks, @primo... you learn something every day! Feb 17, 2014 at 23:52
• @ComFreek That would reverse the order of the digits
– copy
Feb 19, 2014 at 18:39

# Brainf*ck, 98 77

Obviously this isn't for the purpose of winning but what would a competition be if it didnt have a brainfk solution

++++[>++++<-]>>,<[->>++<[->-[>+>>]>[+[-<+>]>+>>]<<<<<]>[-]++++++[->++++++++<]>.[-]>[-<<<+>>>]<<<<]


Since brainfk can only handle 8bit integers and no negatives I guess it doesn't fully abide by the rules but hey I was never in it to win it.

This actually does work for 16-bit input if your interpreter supports

I even got it to output in ascii values

Here is the annotated code:

++[>++++<-]                       preload 8 onto cell 1
>>,<                                input into cell 2
[-                                  iterate over cell 1
>>++<                               put 2 in cell 3
[->-[>+>>]>[+[-<+>]>+>>]<<<<<]      division algorithm: converts {n d} into {0 d_minus_n%d n%d n/d}
>[-]++++++[->++++++++<]>           clears cell 4 and puts 48(ascii of 0) into cell 5
.[-]                                output n%2 and clear it (the bit)
>[-<<<+>>>]                         bring n/2 into cell 2 (to be used for division in next iteration)
<<<<]                               end iterate


Shorter algorithm (77):

+>,>-<[>>[->]++[-<+]-<-]++++++++[->++++++<]>+[->+>+>+>+>+>+>+>+<<<<<<<<]>[.>]


This one can only handle 8bit integers.

The algorithm works by using a binary counter which is actually very short (one increment is >[->]++[-<+]-<- which then lays out the bits. The issue is that it is difficult to print out all of the bits

That last algorithm can be adapted to fit any number of bits at the expense of bytes. To be able to deal with N bit integers, it requires 53+3*N bytes to encode.

examples:

(1 bit) +>,>-<[>>[->]++[-<+]-<-]++++++++[->++++++<]>+[->+<]>[.>]
(2 bit) +>,>-<[>>[->]++[-<+]-<-]++++++++[->++++++<]>+[->+>+<<]>[.>]
(3 bit) +>,>-<[>>[->]++[-<+]-<-]++++++++[->++++++<]>+[->+>+>+<<<]>[.>]
etc


## GolfScript - 17 bytes

~{.1&\2/}16*;]-1%


Not too much more verbose than the built-in ~2base.

• I don't know golfscript but a few sample runs lead me to conclude that you should remove the ~ Feb 16, 2014 at 22:10
• @ace Because the initial input is a string "37", for example, the operation "37" & 1 (in infix) is a set-wise operation. The ~ at the front converts the input to an integer. Feb 17, 2014 at 2:38
• I did my test here golfscript.apphb.com/… does this mean this interpreter is incorrect? (Sorry I really know nothing about golfscript) Feb 17, 2014 at 8:19
• The interpreter is correct; because you've pushed the integer value 10 onto the stack, it is not necessary to evaluate it. However, when read from stdin, the input will be a string (test here). The problem description also explicitly states that the input is a string. Feb 17, 2014 at 8:27

## Mandatory APL answer - 21 22

"01"[1+2|⌊⎕÷2⋆⊖0,⍳15]


Examples:

      "01"[1+2|⌊⎕÷2⋆⊖0,⍳15]
⎕: 0
0000000000000000
"01"[1+2|⌊⎕÷2⋆⊖0,⍳15]
⎕: 13
0000000000001101
"01"[1+2|⌊⎕÷2⋆⊖0,⍳15]
⎕: 9999
0010011100001111
"01"[1+2|⌊⎕÷2⋆⊖0,⍳15]
⎕: -3
1111111111111101
"01"[1+2|⌊⎕÷2⋆⊖0,⍳15]
⎕: 32767
0111111111111111

• You can reduce with almost 50% by using ⎕IO←0, and returning an array of bits instead of a string: 2|⌊⎕÷2*⊖⍳16.
Jun 18, 2016 at 23:09

# Turing Machine Code, 272 bytes

As usual, I'm using the rule table syntax defined here. You can test it on that site or, alternatively, using this java implementation.

A lot of the code is copied from my decimal-to-hex converter here.

0 * * l B
B * * l C
C * 0 r D
D * * r E
E * * r A
A _ * l 1
A * * r *
1 0 9 l 1
1 1 0 l 2
1 2 1 l 2
1 3 2 l 2
1 4 3 l 2
1 5 4 l 2
1 6 5 l 2
1 7 6 l 2
1 8 7 l 2
1 9 8 l 2
1 _ * r Y
Y * * * X
X * _ r X
X _ _ * halt
2 * * l 2
2 _ _ l 3
3 * 1 r 4
3 1 0 l 3
4 * * r 4
4 _ _ r A


Counts down from the input in base 10 while counting up from 0 in base 2. On decrementing zero, it erases the input block and terminates.

## Javascript 59

o='';i=parseInt(prompt());do{o=(i&1)+o}while(i>>=1)alert(o)

• You can use +x instead of parseInt(x) Aug 7, 2016 at 17:01

## Perl, 44

This is my first Perl program ever, so please forgive me if this can be easily golfed down further. Edit: Thank you @primo for taking 7 chars away from my answer.

$x=<>;do{@s=($x&1,@s)}while($x>>=1);print@s  $x=<>;do{push@s,$x&1}while($x>>=1);print reverse@s


The logic is essentially the same as my previous C solution.

Also, uses 64 bits.

• You can save the reverse by constructing the array backwards: @s=($x&1,@s). Feb 16, 2014 at 2:52 • Now that the contest is over, the best I found was 34: $\=$_%2 .$\while$_=$_>>1||<>;print. Or, if command line options count one byte each, 27: 1while$\=$_%2 .$\,$_>>=1}{ using -p. Feb 20, 2014 at 14:22

# Javascript - 56 48 and 36 28 characters

• Does not works with negative numbers.

Thanks to @Blender for shaving 8 characters.

This form takes input and shows output, 48 characters:

x=prompt();for(a="";x;x=~~(x/2))a=x%2+a;alert(a)


If just an instruction that puts in a variable a the binary form of a variable x is needed (and you don't bother in destroying the x value as a side-effect), here it is with 28 characters:

for(a="";x;x=~~(x/2))a=x%2+a

• You can replace Math.floor with ~~, as the range for the numbers is small. Feb 16, 2014 at 11:53
• @Blender Thanks, I knew that there existed some way, just could not find it. Feb 16, 2014 at 12:01
• @Victor I don't know javascript so I might be wrong but at the end when you say a=x%2+a could this be shortened to a+=x%2 ? It works in all languages I know. Feb 16, 2014 at 23:10
• @AlbertRenshaw No, This would be the same as a=a+x%2, but that + is for string concatenation. I.e, your suggestion results in the digits in the backwards order. Feb 17, 2014 at 1:55
• @Victor Ah! Thankyou! Feb 17, 2014 at 3:02

# Python - 61 60 characters

x=input();print"".join("01"[x>>i&1]for i in range(15,-1,-1))

• You can get rid of the space between print and "". Feb 16, 2014 at 11:54
• @Blender I was just about to suggest the same thing :) Feb 16, 2014 at 23:13
• @Blender Ha true, didn't even notice. Done! Feb 17, 2014 at 3:54
• if you call it from the command-line you could leave aside print as it automatically returns the result Aug 18, 2016 at 13:14

## C, 55 chars

Prints an extra leading zero (for the sake of 2 bytes).
Recursion within printf reverses the print order, so the algorithm extracts bits right-to-left but prints left-to-right.

EDIT: Saved a char by using putchar instead of printf.

f(x){(x*=x<0?-printf("-"):1)&&f(x/2);putchar(48+x%2);}


# Dyalog APL, 11 bytes

2|⌊⎕÷2*⌽⍳16


2| The division remainder when halved of
⌊ the rounded down value of
⎕ the input
÷ divided by each of
2* two to the power of each of
⍳16 {0, 1, 2, ..., 15}

Requires ⎕IO←0 which is default on many systems.

TryAPL online!

# Excel, 91 90 81 74

Compatibility note: CONCAT() was available only after later versions of 2016. It replaced CONCATENATE(). Tested in Excel online.

## Formulae

• A1 - Input
• B1 - =A1+4^8*(A1<0) (13) - Convert to 16-bit unsigned equivalent.
• B2 - =1+INT(LOG(B1,2)) (15) - Number of binary digits + 1

## Code (46):

Convert B1 to binary.

=IF(A1=0,0,CONCAT(--ISODD(B1/2^(B2-SEQUENCE(B2)))))


Works in the full 16-bit range.

• I would normally recommend using implicit conversion in th if statement to get something like =IF(A1,CONCAT(--ISODD(B1/2^(B2-ROW(OFFSET(B1,,,B2))))), but as omitting trailing parens is valid you can do better with =A1+4^8*(A1<0 =1+INT(LOG(B1,2 =IF(A1=0,,CONCAT(--ISODD(B1/2^(B2-ROW(OFFSET(B1,,,B2 which would be 82 bytes, if I am counting correctly Jul 20, 2020 at 16:18
• Oh, right, I meant to subtract the trailing parens. Guess I forgot. Jul 20, 2020 at 16:51
• I even stacked the parens at the end for that reason! Unfortunately, with the implicit conversion, I got FALSE as the string, so I would have had to add an extra 2 characters anyway. Otherwise, I could have just omitted the 0. Jul 20, 2020 at 17:00

## C, 81

char b;i=15;main(x){scanf("%d",&x);while(i+1)b[i--]=(x&1)+48,x>>=1;puts(b);}


The output has strictly 16 bits (including padding zeros)

# Apps Script + Google Sheets, 147144 121 bytes

### Script

function j(decNumb){var str='';do{str=String(decNumb%2)+str;decNumb=decNumb/2|0;}while(decNumb>=1);return parseInt(str);}


### Sheet

=j(b1)


Modified version of this script by ZygD.

• Can you remove any spaces? Jun 16, 2016 at 20:06

c 0=0
c n=c(div n 2)*10+mod n 2
b('-':r)='-':b r
b r=show.c.read$r  Call with b "-1023", add main=interact b for a complete program or try it on Ideon. c performs the conversion for positive integers. b r=show.c.read$r converts a string to a number, applies c and converts back to string.
b('-':r)='-':b r strips a possible leading - and re-appends it to the result.

# PowerShell, 598782 70 bytes

+28 bytes for supporting negative numbers.
-12 bytes thanks to @ASCII-only

param($d)$m=$d-lt0;while($d){$n="01"[$d%2]+$n;$d=($d-$d%2)/2}'-'*$m+$n


Try it online!

Adapted from this code. Takes input through a commandline parameter -d.

• What about numbers with sign? Mar 10, 2019 at 5:46
• 73? Mar 11, 2019 at 3:09
• Mar 11, 2019 at 3:14
• oh wait 70 Mar 11, 2019 at 3:22

# APL(NARS), 17 chars, 34 bytes

{2∣⌊⍵÷2*(⍺-1)..0}


It is a copy and modify of Adam answer https://codegolf.stackexchange.com/a/90107 in the way one can add the parameter for the bits lenght, and ⎕IO for this function (here is ⎕IO=1) should have no importance...

  f←{2∣⌊⍵÷2*(⍺-1)..0}
16 f 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
32 f 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
32 f ¯1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
16 f ¯1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
64 f ¯12345678
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 1 1 1 0 0 1 1 1 1 0 1 0 1 1 0 0 1 0


it seeme easy handle the number of bits in this way (I cheked that last result should be right)

# Smalltalk (Smalltalk/X), 63/78

the first version creates an intermediate string (78):

t:=Number readFrom:Stdin.
((15to:1by:-1)collect:[:i|$0+(t>>i&1)]as:String)print  actually, there is no need to create the string; just output the chars (63): t:=Number readFrom:Stdin. 15to:1by:-1 do:[:i|($0+(t>>i&1))print]


mhmh - is there a shorter way to read to a number?

# Python 3.x: 65 characters

b=lambda n:n<2 and'01'[n]or b(n//2)+b(n%2);print(b(int(input())))


# Bash, 44

f=b+=n/2**e%2*10**e,2**e++/n?f=b:f;echo $[f]  Pass an input value to the script through the environment variable n. The decimal representation of the binary result cannot exceed LONG_MAX. This should also be compatible with ksh93 and zsh if b and e are initialized to 0 and proper arithmetic expansion is used. • I don't believe this is valid since it assumes that n is already defined, making it a snippet. That could be fixed by taking input as a command-line argument and setting n to that in your script. Dec 22, 2015 at 20:14 • @quartata Variables in a math context in shell are implicitly zero. For the purpose of golf it makes more sense to do n=127 sh -c '...' than sh -c 'n=$1 ...' _ 127. There's no reason to prefer one over the other in this case as they're both perfectly typical way to pass values. Dec 22, 2015 at 22:14

# C# - 104

string p(int d){var r="";long i=1;while(r.Length<=64){var g=d&i;r=(g!=0)? "1"+r:"0"+r;i=i<<1;}return r;}


This method will convert decimal to binary up to 64 bits.

When executed the above method in Linqpad - rr = p(-32768); rr.Dump();

Output: 01111111111111111111111111111111111111111111111111000000000000000

• The spec calls for "an input string". It looks like this method accepts an int.
– Poke
Jun 16, 2016 at 20:19

# Kotlin, 82 bytes

{s:String->{var i=s.toInt()
var r=""
(0..15).map{r="${i and 1}$r"
i=i shr 1}
r}()}


Try it online!

# Small Basic, 133 bytes

A script that inputs from and outputs to the TextWindow console.

n=TextWindow.Read()
While n>0
c=c+1
x[c]=Math.Remainder(n,2)
n=Math.Floor(n/2)
EndWhile
For i=0To c-1
TextWindow.Write(x[c-i])
EndFor


Try it at SmallBasic.com Requires Silverlight and thus must be run in IE.

I/O is taken/given from the black console.

-22 bytes thanks to @Neil

• Can you not use For i=0To c-1?
– Neil
Jul 13, 2018 at 20:57
• @Neil - I absolutely can. Great catch! Jul 15, 2018 at 21:01

# MATL, 15 17 bytes

t0<?16Ww+]2&\t]x


Try it on MATL Online

TIO

(+2 bytes removing leading 0 for negative numbers, sign bit should be the first bit.)

Output on MATL Online should be read bottom-up (MSB is at the bottom).

The main part is pretty simple: 2&\t = while the value is greater than 0, divide by 2 and accumulate the remainders.

Handling negative numbers and giving them 2's complement representation was the tricky part. In the end I went with the "subtract from $2^N$" method of getting a number's two's complement. Since we're only required to handle values upto -32768, for negative numbers the code creates $2^{16} = 65536$ with 16W, adds the input to that (eg. 65536 + (-42)), which gives something MATLAB sees as a positive number but represents the input's signed binary representation in 16-bit form.

# C (gcc), 50 43 bytes

-7 bytes thanks to ceilingcat.

f(n){printf("-%d"+(~n?n&&f(n/2),1:0),n&1);}


Try it online!

• @ceilingcat Cheers! Aug 4, 2018 at 4:48

# PowerShell, 43 bytes

param($n)15..0|%{$r+='01'[($n-shr$_)%2]}
$r  Try it online! # ><>, 34 33 bytes |!/?=0:,2-}:%2:+***" @"(0: n{\~{  Try it online! # ///, 124 bytes /~/\/\///9/8*~8/7*~7/6*~6/5*~5/4*~4/3*~3/2*~2/1*~1/0*~*0/9*~0~/*/>Oⅼ~ⅼ>/ⅼ~ⅼO/Oⅼ~Oⅼⅼ/ⅼ\O~Oⅼ/_ⅼ~_~/>O/>~>~  Try it online! Could be considered cheating, Outputs ⅼ and O instead of 1 and 0, due to the mechanics of ///. Uses examples from the wiki. # Perl 5, 26 bytes Produces an additional leading 0 which can be avoided with two additional bytes (appending }{) $\=($_&1).$\;redo if\$_>>=1


Try it online!

# Clojure 129 bytes#

Golfed version:

(defn p[n](loop[m 32768](if(> m 0)(do(if(= 0(bit-and m n))(print"0")(print"1"))(recur(unsigned-bit-shift-right m 1)))(println))))


Ungolfed:

(defn print-as-binary [n]