Number Values Changing When ToString() Applied

I am noticing something very strange when testing one of my functions that checks the validity of numbers, I first noticed it when testing the 'number.toString()[0]'. If I console

Solution 1:

010 is treated as an octal notation because of the leading 0, as well as 0x10 will be treated as an hexadecimal notation. The octal numeral system uses the digits 0 to 7. Thus, 019 gives 19 because 9 is not an octal digit. Here some decimal numbers and their octal notations:

1  1 | 5  5 | 9  11 | 13 15
2  2 | 6  6 | 10 12 | 14 16
3  3 | 7  7 | 11 13 | 15 17
4  4 | 8 10 | 12 14 | 16 20

As you can see, since we have only 8 digits available (0, 1, 2, 3, 4, 5, 6, 7), 8 becomes 10 and 16 (8+8) becomes 20 (10+10). To make things even more clear, let's see how to count with 10 digits (as usual) then with 8 digits.

Using 10 digits:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, no more digits
nevermind, add 1 to the tenths and restart from 0
10, 11, 12, 13, 14, 15, 16, 17, 18, 19, no more digits
nevermind, add 1 to the tenths and restart from 0
20, 21, etc...

Using 8 digits:

0, 1, 2, 3, 4, 5, 6, 7, no more digits
nevermind, add 1 to the "tenths" and restart from 0
10, 11, 12, 13, 14, 15, 16, 17, no more digits
nevermind, add 1 to the "tenths" and restart from 0
20, 21, etc...

The same applies to binary numbers:

   0,   1, no more digits
  10,  11, no more digits
 100, 101, no more digits
 110, 111, no more digits
1000, etc...

Let's compare with the decimal notation:

1    1 | 5  101 |  9 1001
2   10 | 6  110 | 10 1010
3   11 | 7  111
4  100 | 8 1000

Related stuffs: https://stackoverflow.com/a/32107058/1636522 :-)

Solution 2:

Number is a 64bit floating point representation of a number. It does not hold the digits as a array of characters so the leading zero is not available. String holds an array of characters and thus the leading 0 is not lost

JavaScript allows for transparent type conversion if possible thus the String "0111" == to the Number 111. So if you write the code "0111" == 111 it will return true.

Javascript provides two equality operators == and the strict equality === the second requires that both side are the same type so the Number(111) === String("111") will return false as they are not the same type. The same applies for inequality operators != and !==