I want to define a BigInt number in JavaScript. But when I assign it, the wrong number is stored. In fact 1 is added to the number when storing.
let num = BigInt(0b0000111111111111111111111111111111111111111111111111111111111111)
console.log(num) // Output: 1152921504606846976n
console.log(num.toString(2)) // Output: 1000000000000000000000000000000000000000000000000000000000000
So the number stored is 1152921504606846976, but it should be 11529215046068469765. Why is that?
Converting a Number to a BigInt can't create bits that weren't there before.
0b1 (just like 1) is a Number literal, so it creates a Number.
0b1n (just like 1n) is a BigInt literal, so it creates a BigInt.
By writing BigInt(0b1), you're first creating a Number and then converting that to a BigInt. As long as the value is 1, that works just fine; once the value exceeds what you can losslessly store in a Number [1], you'll see that the value of the final BigInt won't match the literal you wrote down. Whether you use binary (0b...), decimal, or hex (0x...) literals doesn't change any of that.
(And just to be extra clear: there's no reason to write BigInt(123n), just like you wouldn't write Number(123). 123n already is a BigInt, so there's nothing to convert.)
A simple non-BigInt way to illustrate what's happening is to enter 12345678901234567890 into your favorite browser's DevTools console: you can specify Number literals of any length you want, but they'll be parsed into an IEEE754 64-bit "double", which has limited precision. Any extra digits in the literal simply can't be stored, though of course each digit's presence affects the magnitude of the number.
[1] Side note: this condition is more subtle than just saying that Number.MAX_SAFE_INTEGER is the threshold, though that constant is related to the situation: any integral number below MAX_SAFE_INTEGER can be stored losslessly, but there are plenty of numbers above MAX_SAFE_INTEGER that can also be represented exactly. Random example: 1e20.