Javascript right shift a negative number

Question

Here is the snippet:

var i = 101;
console.log('101: ' +  i.toString(2));
console.log('101 >> 1: ' + (i >> 1).toString(2));

var l = -101;
console.log('-101: ' + l.toString(2));
console.log('-101 >> 1: ' + (l >> 1).toString(2));'

Output:

"101: 1100101"
"101 >> 1: 110010"
"-101: -1100101"
"-101 >> 1: -110011"

Why -101 >> 1 is -110011 instead of -110010 ?

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Update: the book Professional javaScript for Web Developers explains how js stores a negative number:

1. get the binary representation of the absolute value of the negative number
2. replace 0s with 1s and 1s with 0s
3. add 1 to the result of step 2

So in my case -101 >> 1 , we first convert -101 to its binary representation:

1. The binary representation of Math.abs(-101) is:

   0000 0000 0000 0000 0000 0000 0110 0101

2. invert the 0s and 1s:

   1111 1111 1111 1111 1111 1111 1001 1010

3. add 1 to the end:

   1111 1111 1111 1111 1111 1111 1001 1011

4. Now, shift it to the right by 1:

   1111 1111 1111 1111 1111 1111 1100 1101

The binary above should be the correct result of -101 >> 1 , but when logging a negative number's binary representation, Javascript simply puts a negative sign in front of the binary representation of the positive number:

var x = 15;
console.log(x.toString(2)); // output: 1111

var y = -15;
console.log(y.toString(2)); // output: -1111

For our example, this means that when logging the result of -101 >> 1 , JS will output minus sign + the binary representation of the positive number . But the positive number is not 101 >> 1 because 101 >> 1 gives you:

(101 >> 1).toString(2);  // output: 110010
(-101 >> 1).toString(2); // output: -110011, not -110010!

To get the correct result, we have to reverse the aforementioned step 1-3:

1111 1111 1111 1111 1111 1111 1100 1101   // this is the result we get from step 4

Reverse step 3 by subtracting 1, we get:

1111 1111 1111 1111 1111 1111 1100 1100

Reverse step 2 by invert 0s and 1s:

0000 0000 0000 0000 0000 0000 0011 0011

Reverse step 1 by converting this binary to integer:

parseInt(110011, 2); // output: 51

Finally, when JS logs the result of -101 >> 1 , it will be minus sign + the binary representation of 51 which is:

(51).toString(2);        // output:  110011
(-101 >> 1).toString(2); // output: -110011

Answer 1

Remember that negative numbers are stored as a 2s-complement. For simplicity, let's say it's a 1-byte signed integer, then -101 would be stored as

1 0000 0000 (256)
- 0110 0101 (101)
= 1001 1011 (155 if it were unsigned, -101 in signed)

When bit-shifting a negative number, you right-pad with 1 s instead of 0 s (otherwise you'd lose the sign bit), so the result is:

  1001 1011
       >> 1
= 1100 1101

That is 205 if it were an unsigned integer. Then 2s-complement it back to solve 256 - x = 205 => x = 51

Ta-da? :D