JavaScript的内置Number（）方法似乎返回了一个不正确的值

Question

I've made a program to convert bases of numbers. I thought that, in the event that there are no characters AF in the output, it would be convenient to return the number as a Number instead of a String (even though I'd be returning base 2 numbers as regular decimal numbers, whatever).

For some reason, when I converted A3B2 ₃₂ to Binary (which should be 1010000110101100100 ₂ [ Wolfram|Alpha source]), I got 1010000110101100200 . There's a two in there, that isn't binary! The final line of code which returns the value is:

return (toBase <= 10) ? Number(result) : result;

This worked properly for basically all tests, until I decided to use that base-32 number above. I thought my program was doing the division/remainder step incorrect, so I had it print out the result just before it returns the value. It was correctly giving out 1010000110101100100 . So, I tested the Number() method directly in Chrome's console. This is what happened:

> Number("1010000110101100100")
> 1010000110101100200

Am I misunderstanding what the Number() method does? Why is it converting a string made up of all Ones and Zeroes to a number with Ones, Zeroes, and Twos ?

Answer 1

What you're doing when calling Number("1010000110101100100") is passing a string, which it is trying to turn it into a number, but that number is higher than JavaScript can count, which is 9,007,199,254,740,991 (also known as Number.MAX_SAFE_INTEGER )

Basically, any number over 9,007,199,254,740,991 can't reliably be used because JavaScript uses double-precision floating-point format numbers as specified in IEEE 754

Here's some examples, the following input numbers "should" be the same as the output, but aren't because they've gone over the MAX_SAFE_INTEGER. Some are, but it's not reliable as demonstrated in the Bonus Fun With LARGE Numbers section below.

Number("9007199254740992") // 9007199254740992
Number("9007199254740993") // 9007199254740992
Number("9007199254740994") // 9007199254740994
Number("9007199254740995") // 9007199254740996
Number("9007199254740996") // 9007199254740996
Number("9007199254740997") // 9007199254740996
Number("9007199254740998") // 9007199254740998
Number("9007199254740999") // 9007199254741000

If you still want to convert hex to binary, you need to use parseInt and Number.prototype.toString and keep it as a string.

 const hex = "A3B2"; const binary = parseInt(hex, 16).toString(2); console.log(binary); 

Bonus Fun With LARGE Numbers

The following is true!

 console.log(9007199254740992 === 9007199254740993); console.log(1010000110101100200 === 1010000110101100100) 

Documentation

https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Number

https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Number/MAX_SAFE_INTEGER

https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/parseInt

https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Number/toString

Answer 2

@AnonymusSB said is right. i want add few details to it.

So when you Number(value) it internally calls ToNumber to calculate the value. when you supply a string. it have a two step process to change it number.

1. First it calculate the Mathematical value (MV) of the string.
2. In second process it rounds up the calculated value.(when you exceed the limit of Math.MAX_SAFE_INTEGER it round of the number).

 console.log(Number("9007199254740996")) console.log(Number("9007199254740997"), "rounded down") console.log(Number("9007199254740998")) console.log(Number("9007199254740999") ,"rounded up") 

EcmaScript