According to subsection 11.4.8 of the ECMAScript 5.1 standard:

The production UnaryExpression : ~ UnaryExpression is evaluated as follows:

1. Let expr be the result of evaluating UnaryExpression.
2. Let oldValue be ToInt32(GetValue(expr)).
3. Return the result of applying bitwise plement to oldValue. The result is a signed 32-bit integer.

The ~ operator will invoke the internal method ToInt32. In my understanding ToInt32(1) and ToInt32(-1) will return the same value 1 , but why does ~-1 equal 0 and ~1 equal -2?

Now my question is why ToInt32(-1) equals -1? subsection 9.5 of the ECMAScript 5.1 standard:

The abstract operation ToInt32 converts its argument to one of 2³² integer values in the range −2³¹ through 2³¹−1, inclusive. This abstract operation functions as follows:

1. Let number be the result of calling ToNumber on the input argument.
2. If number is NaN, +0, −0, +∞, or −∞, return +0.
3. Let posInt be sign(number) * floor(abs(number)).
4. Let int32bit be posInt modulo 2³²; that is, a finite integer value k of Number type with positive sign and less than 2³² in magnitude such that the mathematical difference of posInt and k is mathematically an integer multiple of 2³².
5. If int32bit is greater than or equal to 2³¹, return int32bit − 2³², otherwise return int32bit.

when the argument is -1,according to 9.5, in step 1 number will still be -1, skip step2 in step 3 posInt will be -1 in step 4 int32bit will be 1 in step 5 it will return 1

which step is wrong?

According to subsection 11.4.8 of the ECMAScript 5.1 standard:

The production UnaryExpression : ~ UnaryExpression is evaluated as follows:

1. Let expr be the result of evaluating UnaryExpression.
2. Let oldValue be ToInt32(GetValue(expr)).
3. Return the result of applying bitwise plement to oldValue. The result is a signed 32-bit integer.

The ~ operator will invoke the internal method ToInt32. In my understanding ToInt32(1) and ToInt32(-1) will return the same value 1 , but why does ~-1 equal 0 and ~1 equal -2?

Now my question is why ToInt32(-1) equals -1? subsection 9.5 of the ECMAScript 5.1 standard:

The abstract operation ToInt32 converts its argument to one of 2³² integer values in the range −2³¹ through 2³¹−1, inclusive. This abstract operation functions as follows:

1. Let number be the result of calling ToNumber on the input argument.
2. If number is NaN, +0, −0, +∞, or −∞, return +0.
3. Let posInt be sign(number) * floor(abs(number)).
4. Let int32bit be posInt modulo 2³²; that is, a finite integer value k of Number type with positive sign and less than 2³² in magnitude such that the mathematical difference of posInt and k is mathematically an integer multiple of 2³².
5. If int32bit is greater than or equal to 2³¹, return int32bit − 2³², otherwise return int32bit.

when the argument is -1,according to 9.5, in step 1 number will still be -1, skip step2 in step 3 posInt will be -1 in step 4 int32bit will be 1 in step 5 it will return 1

which step is wrong?

• javascript
• operators
• bitwise-operators
• ecmascript-5

• 1 ToIn32(-1) should yield -1 according to ecma-international/ecma-262/5.1/#sec-9.5 – BartoszKP Commented Aug 15, 2013 at 17:06
• Your understanding is wrong and was corrected in your previous question... (more specifically, in my answer) – Esailija Commented Aug 15, 2013 at 17:22
• possible duplicate of what is the result of 'x modulo y'? – Esailija Commented Aug 15, 2013 at 17:23
• Found this helpful when looking up information about tilde. javascriptturnsmeon./the-tilde-operator-in-javascript. Basically ~x === -(x + 1) – awbergs Commented Aug 15, 2013 at 17:27

3 Answers 3

The -1 in 32-bit integer

1111 1111 1111 1111 1111 1111 1111 1111

So ~-1 will be

0000 0000 0000 0000 0000 0000 0000 0000

Which is zero.

The 1 in 32-bit integer

0000 0000 0000 0000 0000 0000 0000 0001

So ~1 will be

1111 1111 1111 1111 1111 1111 1111 1110

Which is -2.

You should read about two's plement to understand the display of negative integer in binary-base.

Where did you get the idea that ToInt32(-1) evaluates to 1? It evaluates to -1, which in 32-bit, two's plement binary representation, is all bits set to 1. When you apply the ~ operator, every bit then bees 0, which is the representation of 0 in 32-bit, two's plement binary.

The representation of 1 is all bits 0 except for bit 0. When the bits are inverted, the result is all bits 1 except for bit 0. This happens to be the two's plement representation of -2. (To see this, just subtract 1 from the two's plement representation of -1.)

• ToInt32(1) will return 1
• ToInt32(-1) will return -1
• -1 is represented as a signed 32-bit integer by having all 32 bits set. The bitwise plement of that is all bits clear, thus ~-1 yields 0
• 1 is represented as a signed 32-bit integer by having all bits clear except the bottom bit. The bitwise plement of that has all bits set except the bottom bit, which is the signed 32-bit integer representation of the value -2. Thus, ~1 yields -2