Cheng Cheng - 7 months ago 9
Javascript Question

Javascript right shift a negative number

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
?




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

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 1s instead of 0s (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