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?

Answer 1

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))

Answer 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