How do I convert an integer to binary in JavaScript?
I’d like to see integers, positive or negative, in binary.
Rather like this question, but for JavaScript.
Answers:
function dec2bin(dec){
return (dec >>> 0).toString(2);
}
dec2bin(1); // 1
dec2bin(-1); // 11111111111111111111111111111111
dec2bin(256); // 100000000
dec2bin(-256); // 11111111111111111111111100000000
You can use Number.toString(2) function, but it has some problems when representing negative numbers. For example, (-1).toString(2) output is "-1".
To fix this issue, you can use the unsigned right shift bitwise operator (>>>) to coerce your number to an unsigned integer.
If you run (-1 >>> 0).toString(2) you will shift your number 0 bits to the right, which doesn't change the number itself but it will be represented as an unsigned integer. The code above will output "11111111111111111111111111111111" correctly.
This question has further explanation.
-3 >>> 0(right logical shift) coerces its arguments to unsigned integers, which is why you get the 32-bit two's complement representation of -3.
Try
num.toString(2);
The 2 is the radix and can be any base between 2 and 36
source here
UPDATE:
This will only work for positive numbers, Javascript represents negative binary integers in two's-complement notation. I made this little function which should do the trick, I haven't tested it out properly:
function dec2Bin(dec)
{
if(dec >= 0) {
return dec.toString(2);
}
else {
/* Here you could represent the number in 2s compliment but this is not what
JS uses as its not sure how many bits are in your number range. There are
some suggestions https://stackoverflow.com/questions/10936600/javascript-decimal-to-binary-64-bit
*/
return (~dec).toString(2);
}
}
I had some help from here
The binary in 'convert to binary' can refer to three main things. The positional number system, the binary representation in memory or 32bit bitstrings. (for 64bit bitstrings see Patrick Roberts' answer)
1. Number System
(123456).toString(2) will convert numbers to the base 2 positional numeral system. In this system negative numbers are written with minus signs just like in decimal.
2. Internal Representation
The internal representation of numbers is 64 bit floating point and some limitations are discussed in this answer. There is no easy way to create a bit-string representation of this in javascript nor access specific bits.
3. Masks & Bitwise Operators
MDN has a good overview of how bitwise operators work. Importantly:
Bitwise operators treat their operands as a sequence of 32 bits (zeros and ones)
Before operations are applied the 64 bit floating points numbers are cast to 32 bit signed integers. After they are converted back.
Here is the MDN example code for converting numbers into 32-bit strings.
function createBinaryString (nMask) {
// nMask must be between -2147483648 and 2147483647
for (var nFlag = 0, nShifted = nMask, sMask = ""; nFlag < 32;
nFlag++, sMask += String(nShifted >>> 31), nShifted <<= 1);
return sMask;
}
createBinaryString(0) //-> "00000000000000000000000000000000"
createBinaryString(123) //-> "00000000000000000000000001111011"
createBinaryString(-1) //-> "11111111111111111111111111111111"
createBinaryString(-1123456) //-> "11111111111011101101101110000000"
createBinaryString(0x7fffffff) //-> "01111111111111111111111111111111"
A simple way is just...
Number(42).toString(2);
// "101010"
This answer attempts to address inputs with an absolute value in the range of 214748364810 (231) – 900719925474099110 (253-1).
In JavaScript, numbers are stored in 64-bit floating point representation, but bitwise operations coerce them to 32-bit integers in two's complement format, so any approach which uses bitwise operations restricts the range of output to -214748364810 (-231) – 214748364710 (231-1).
However, if bitwise operations are avoided and the 64-bit floating point representation is preserved by using only mathematical operations, we can reliably convert any safe integer to 64-bit two's complement binary notation by sign-extending the 53-bit twosComplement:
function toBinary (value) {
if (!Number.isSafeInteger(value)) {
throw new TypeError('value must be a safe integer');
}
const negative = value < 0;
const twosComplement = negative ? Number.MAX_SAFE_INTEGER + value + 1 : value;
const signExtend = negative ? '1' : '0';
return twosComplement.toString(2).padStart(53, '0').padStart(64, signExtend);
}
function format (value) {
console.log(value.toString().padStart(64));
console.log(value.toString(2).padStart(64));
console.log(toBinary(value));
}
format(8);
format(-8);
format(2**33-1);
format(-(2**33-1));
format(2**53-1);
format(-(2**53-1));
format(2**52);
format(-(2**52));
format(2**52+1);
format(-(2**52+1));.as-console-wrapper{max-height:100%!important}For older browsers, polyfills exist for the following functions and values:
As an added bonus, you can support any radix (2–36) if you perform the two's complement conversion for negative numbers in ?64 / log2(radix)? digits by using BigInt:
function toRadix (value, radix) {
if (!Number.isSafeInteger(value)) {
throw new TypeError('value must be a safe integer');
}
const digits = Math.ceil(64 / Math.log2(radix));
const twosComplement = value < 0
? BigInt(radix) ** BigInt(digits) + BigInt(value)
: value;
return twosComplement.toString(radix).padStart(digits, '0');
}
console.log(toRadix(0xcba9876543210, 2));
console.log(toRadix(-0xcba9876543210, 2));
console.log(toRadix(0xcba9876543210, 16));
console.log(toRadix(-0xcba9876543210, 16));
console.log(toRadix(0x1032547698bac, 2));
console.log(toRadix(-0x1032547698bac, 2));
console.log(toRadix(0x1032547698bac, 16));
console.log(toRadix(-0x1032547698bac, 16));.as-console-wrapper{max-height:100%!important}If you are interested in my old answer that used an ArrayBuffer to create a union between a Float64Array and a Uint16Array, please refer to this answer's revision history.
A solution i'd go with that's fine for 32-bits, is the code the end of this answer, which is from developer.mozilla.org(MDN), but with some lines added for A)formatting and B)checking that the number is in range.
Some suggested x.toString(2) which doesn't work for negatives, it just sticks a minus sign in there for them, which is no good.
Fernando mentioned a simple solution of (x>>>0).toString(2); which is fine for negatives, but has a slight issue when x is positive. It has the output starting with 1, which for positive numbers isn't proper 2s complement.
Anybody that doesn't understand the fact of positive numbers starting with 0 and negative numbers with 1, in 2s complement, could check this SO QnA on 2s complement. What is “2's Complement”?
A solution could involve prepending a 0 for positive numbers, which I did in an earlier revision of this answer. And one could accept sometimes having a 33bit number, or one could make sure that the number to convert is within range -(2^31)<=x<2^31-1. So the number is always 32bits. But rather than do that, you can go with this solution on mozilla.org
Patrick's answer and code is long and apparently works for 64-bit, but had a bug that a commenter found, and the commenter fixed patrick's bug, but patrick has some "magic number" in his code that he didn't comment about and has forgotten about and patrick no longer fully understands his own code / why it works.
Annan had some incorrect and unclear terminology but mentioned a solution by developer.mozilla.org https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Operators/Bitwise_Operators This works for 32-bit numbers.
The code is pretty compact, a function of three lines.
But I have added a regex to format the output in groups of 8 bits. Based on How to print a number with commas as thousands separators in JavaScript (I just amended it from grouping it in 3s right to left and adding commas, to grouping in 8s right to left, and adding spaces)
And, while mozilla made a comment about the size of nMask(the number fed in)..that it has to be in range, they didn't test for or throw an error when the number is out of range, so i've added that.
I'm not sure why they named their parameter 'nMask' but i'll leave that as is.
//https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Operators/Bitwise_Operators
function createBinaryString(nMask) {
// nMask must be between -2147483648 and 2147483647
if (nMask > 2**31-1)
throw "number too large. number shouldn't be > 2**31-1"; //added
if (nMask < -1*(2**31))
throw "number too far negative, number shouldn't be < 2**31") //added
for (var nFlag = 0, nShifted = nMask, sMask = ''; nFlag < 32;
nFlag++, sMask += String(nShifted >>> 31), nShifted <<= 1);
sMask=sMask.replace(/\B(?=(.{8})+(?!.))/g, " ") // added
return sMask;
}
createBinaryString(-1)
"11111111 11111111 11111111 11111111"
createBinaryString(1024)
"00000000 00000000 00000100 00000000"
createBinaryString(-2)
"11111111 11111111 11111111 11111110"
createBinaryString(-1024)
"11111111 11111111 11111100 00000000"
You can write your own function that returns an array of bits. Example how to convert number to bits
Divisor| Dividend| bits/remainder
2 | 9 | 1
2 | 4 | 0
2 | 2 | 0
~ | 1 |~
example of above line: 2 * 4 = 8 and remainder is 1 so 9 = 1 0 0 1
function numToBit(num){
var number = num
var result = []
while(number >= 1 ){
result.unshift(Math.floor(number%2))
number = number/2
}
return result
}
Read remainders from bottom to top. Digit 1 in the middle to top.
I used a different approach to come up with something that does this. I've decided to not use this code in my project, but I thought I'd leave it somewhere relevant in case it is useful for someone.
- Doesn't use bit-shifting or two's complement coercion.
- You choose the number of bits that comes out (it checks for valid values of '8', '16', '32', but I suppose you could change that)
- You choose whether to treat it as a signed or unsigned integer.
- It will check for range issues given the combination of signed/unsigned and number of bits, though you'll want to improve the error handling.
- It also has the "reverse" version of the function which converts the bits back to the int. You'll need that since there's probably nothing else that will interpret this output :D
function intToBitString(input, size, unsigned) {
if ([8, 16, 32].indexOf(size) == -1) {
throw "invalid params";
}
var min = unsigned ? 0 : - (2 ** size / 2);
var limit = unsigned ? 2 ** size : 2 ** size / 2;
if (!Number.isInteger(input) || input < min || input >= limit) {
throw "out of range or not an int";
}
if (!unsigned) {
input += limit;
}
var binary = input.toString(2).replace(/^-/, '');
return binary.padStart(size, '0');
}
function bitStringToInt(input, size, unsigned) {
if ([8, 16, 32].indexOf(size) == -1) {
throw "invalid params";
}
input = parseInt(input, 2);
if (!unsigned) {
input -= 2 ** size / 2;
}
return input;
}
// EXAMPLES
var res;
console.log("(uint8)10");
res = intToBitString(10, 8, true);
console.log("intToBitString(res, 8, true)");
console.log(res);
console.log("reverse:", bitStringToInt(res, 8, true));
console.log("---");
console.log("(uint8)127");
res = intToBitString(127, 8, true);
console.log("intToBitString(res, 8, true)");
console.log(res);
console.log("reverse:", bitStringToInt(res, 8, true));
console.log("---");
console.log("(int8)127");
res = intToBitString(127, 8, false);
console.log("intToBitString(res, 8, false)");
console.log(res);
console.log("reverse:", bitStringToInt(res, 8, false));
console.log("---");
console.log("(int8)-128");
res = intToBitString(-128, 8, false);
console.log("intToBitString(res, 8, true)");
console.log(res);
console.log("reverse:", bitStringToInt(res, 8, true));
console.log("---");
console.log("(uint16)5000");
res = intToBitString(5000, 16, true);
console.log("intToBitString(res, 16, true)");
console.log(res);
console.log("reverse:", bitStringToInt(res, 16, true));
console.log("---");
console.log("(uint32)5000");
res = intToBitString(5000, 32, true);
console.log("intToBitString(res, 32, true)");
console.log(res);
console.log("reverse:", bitStringToInt(res, 32, true));
console.log("---");This is my code:
var x = prompt("enter number", "7");
var i = 0;
var binaryvar = " ";
function add(n) {
if (n == 0) {
binaryvar = "0" + binaryvar;
}
else {
binaryvar = "1" + binaryvar;
}
}
function binary() {
while (i < 1) {
if (x == 1) {
add(1);
document.write(binaryvar);
break;
}
else {
if (x % 2 == 0) {
x = x / 2;
add(0);
}
else {
x = (x - 1) / 2;
add(1);
}
}
}
}
binary();
This is the solution . Its quite simple as a matter of fact
function binaries(num1){
var str = num1.toString(2)
return(console.log('The binary form of ' + num1 + ' is: ' + str))
}
binaries(3
)
/*
According to MDN, Number.prototype.toString() overrides
Object.prototype.toString() with the useful distinction that you can
pass in a single integer argument. This argument is an optional radix,
numbers 2 to 36 allowed.So in the example above, we’re passing in 2 to
get a string representation of the binary for the base 10 number 100,
i.e. 1100100.
*/
One more alternative
const decToBin = dec => {
let bin = '';
let f = false;
while (!f) {
bin = bin + (dec % 2);
dec = Math.trunc(dec / 2);
if (dec === 0 ) f = true;
}
return bin.split("").reverse().join("");
}
console.log(decToBin(0));
console.log(decToBin(1));
console.log(decToBin(2));
console.log(decToBin(3));
console.log(decToBin(4));
console.log(decToBin(5));
console.log(decToBin(6));
This is how I manage to handle it:
const decbin = nbr => {
if(nbr < 0){
nbr = 0xFFFFFFFF + nbr + 1
}
return parseInt(nbr, 10).toString(2)
};
got it from this link: https://locutus.io/php/math/decbin/
we can also calculate the binary for positive numbers as below:
function toBinary(n){
let binary = "";
while(Math.ceil(n/2) > 0){
binary = n%2 + binary;
n = Math.floor(n/2);
}
return binary;
}
console.log(toBinary(7));