javascript bitwise xor producing inconsistent result

Question

I am using bitwise operations in javascript but I have noticed something that appears inconsistent.

Right now, I'm using the XOR (^) operation. When I do '0101'^'0001' , I get 4, which makes sense since 4 = 0100 in binary. But when I do '10001'^'01111' , I get 9030, when I think I should get 11110. The format is, to best that I can tell, the same; only the strings are different.

console.log(5^1); //4
console.log('0101'^'0001'); // 100 = 4

console.log(17^15); //30
console.log('10001'^'01111'); //9030...why? shouldn't it be '11110'?

Why is this code producing this result?

Now, If I do this:

console.log(('0b'+'10001')^('0b' + '01111')); //30

Why did I have to add '0b' to specify that the strings were binary sequences when doing bitwise ops on 17 and 15, but not with 5 and 1?

Answer 1

You are using the ^ operator on strings. When using any numerical operator on a string JavaScript will implicitly convert the string to a number. Adding 0b tells JavaScript to treat your number as a binary or base 2 number.

Otherwise, by default they will be converted to decimal or base 10 values.

Do operations on binary values represented in a string you have to convert your values to numerical base 2 values first.

You can verify in a calculator 10,001^1111 = 9030.

In binary 1111=15 and 10001=17. 15^17= 30 which is 11110‬ in binary.

101 Xor 1 is a special case, In decimal 101 Xor 1 = 100. In Binary 101 = 5 and 5 Xor 1 = 4 which is written out in binary as 100.

Answer 2

As has been pointed out already, you are not using binary numbers. Use the 0b prefix for binary numbers and toString(2) to convert back:

console.log((0b10001 ^ 0b01111).toString(2));
11110

The first example just works because 1 in decimal is the same as 1 in binary. The result is 100 (decimal) though, not 4. Javascript doesn't store the number format internally.