Javascript Decimal to Binary - 64 bit

Question

The binary for the decimal -805306368 is:

11111111111111111111111111111111 11010000000000000000000000000000

However, in Javascript I get the following:

var str = parseInt(-805306368).toString(2);
document.write(str);

-110000000000000000000000000000

Can anyone explain how to parse the 64 bit binary string from this decimal?

There's a little semantic funny business in your question. -805306368 in base 10 is exactly what you're getting: -110000000000000000000000000000 in base 2. What you're looking for is the two's-complement representation. — Carl Norum
– Carl Norum, Commented Jun 7, 2012 at 17:16

Teocci · Accepted Answer · 2022-07-07 01:24:30Z

14

JavaScript does not use the two's-complement representation, it uses the hyphen - character in front of the string to represent negative numbers. That's because two's-complement representation requires to know the length of bits. When turning a two's-complement number with a certain number of bits into one with more bits (e.g., when copying from a one-byte variable to a two-byte variable), the most-significant bit must be repeated in all the extra bits.

To get the expected result, you could invert each bit but it doesn't provide the result we want:

>>> (~-805306368).toString(2)
"101111111111111111111111111111"

Yet, JavaScript does all binary operations on 32-bit integers, so this won't work for bigger (or smaller) numbers and at least will be very confusing. So, you would need to implement your own formatting algorithm.

// example of 32-bit-conversion:
>>> (~parseInt("1111111111111111111111111111111",2)).toString(2)
"-10000000000000000000000000000000"
>>> (~parseInt("11111111111111111111111111111111",2)).toString(2)
"0"

My Implementation:

function get64binary(int) {
  if (int >= 0)
    return int
      .toString(2)
      .padStart(64, "0");
  else
    return (-int - 1)
      .toString(2)
      .replace(/[01]/g, d => +!+d) // hehe: inverts each char
      .padStart(64, "1");
}

console.log(get64binary(805306368))
console.log(get64binary(-805306368))

edited Jul 7, 2022 at 1:24

Teocci

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answered Jun 7, 2012 at 17:29

Bergi

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4 Comments

StuR Over a year ago

Yes, this is exactly what I was after. Thanks.

StuR Over a year ago

I've just realised the same. What I expect to be returned is "11010000000000000000000000000000" (the first 32 bits)

StuR Over a year ago

Ok, any pointers on implementing my own formatting algorithm - or an example in another language I can use for guidance?

StuR Over a year ago

Perfect, your function works great. Thanks very much for your help, if Carlsberg did answers.. :)

Sune Rasmussen · Accepted Answer · 2012-06-07 17:17:34Z

2

You can use parseInt() again. It has an optional second parameter, that enables you to specify the radix (or base) of the number in the string you are trying to parse.

Such as: parseInt("-110000000000000000000000000000", 2) // gives -805306368

answered Jun 7, 2012 at 17:17

Sune Rasmussen

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