Bitwise addition of opposite signs

Question

int main(){
        int a = 10, b = -2;
        printf("\n %d \n",a^b);
        return 0;
}

This program outputs -12. I could not understand how. Please explain.

0111 1110 -> 2's complement of -2
0000 1010 -> 10
---------
0111 0100

This no seems to be greater than -12 and is +ve. But how did I get the o/p as -12 ?

Hint: what is 2's complement of 12 ? – Marian Apr 26 '14 at 10:13 — Marian, Apr 26 '14 at 10:13
-2 is actualy 11111...10 – Coldsteel48 Apr 26 '14 at 10:13 — Coldsteel48, Apr 26 '14 at 10:13

ajay · Accepted Answer · 2014-04-29T07:49:40.363

2

To find the two's complement of a negative integer, first find the binary representation of its magnitude. Then flip all its bits, i.e., apply the bitwise NOT operator !. Then add 1 to it. Therefore, we have

2       -->  0000 0000 0000 0010
~2      -->  1111 1111 1111 1101  // flip all the bits
~2 + 1  -->  1111 1111 1111 1110  // add 1

Therefore, the binary representation of -2 in two's complement is

1111 1111 1111 1110

Now, assuming the size of int is 4, the representation of a and b in two's complement is -

a -->        0000 0000 0000 1010  --> 10
b -->        1111 1111 1111 1110  --> -2
a^b -->      1111 1111 1111 0100  --> -12

The operator ^ is the bitwise XOR, or exclusive OR operator. If operates on the corresponding bits of a and b and evaluates to 1 only when the bits are not both 0 or both 1, else it evaluate to 0.

edited Apr 29 '14 at 07:49

answered Apr 26 '14 at 10:15

ajay

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1111 1111 1111 0100 - Is this no -12 ?. what happened to the bits set before it. If MSB is set with 1, we consider it as a minus no. What happens to the bits set from 5th bit till the 15th bit. – Angus Apr 26 '14 at 10:21
@Angus that's sign extension. `10100` is -12 and adding the sign bit to the left of the number doesn't change its value – phuclv Apr 26 '14 at 10:24
@Angus Here's the rule. If the MSB is `1`, then the number is negative. To get its modulus, flip all the bits and add 1. – ajay Apr 26 '14 at 10:26
@Roma-MT Yes, `(!(a^b))+1` would give the magnitude since `a^b` is negative. – ajay Apr 26 '14 at 10:30
@Lưu Vĩnh Phúc: I couldnt still get it. can you please explain in detail. – Angus Apr 26 '14 at 10:31
1

@ajay add it to your answer ! it will be helpful for future users ! – Coldsteel48 Apr 26 '14 at 10:33
@Ajay: Thanks. I could get why -12. – Angus Apr 26 '14 at 10:38
1

@ajay the bitwise not should be `~`, not `!`. So that's `~2 + 1` – phuclv Apr 29 '14 at 07:26
@LưuVĩnhPhúc Yes, right! I somehow mixed it. fixed now. Thanks much :) – ajay Apr 29 '14 at 07:50

score 2 · Answer 2 · answered Apr 26 '14 at 10:15

2

Seems legit!

1111 1110   (-2)
xor
0000 1010   (10)
=
1111 0100   (-12)

answered Apr 26 '14 at 10:15

Coldsteel48

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phuclv · Answer 3 · 2019-06-04T03:52:07.950

1

^ is the bitwise XOR, not power

a = 10 = 0000 1010
b = -2 = 1111 1110
──────────────────
a^b    = 1111 0100 = -12

edited Jun 04 '19 at 03:52

answered Apr 26 '14 at 10:15

phuclv

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score 0 · Answer 4 · edited Apr 26 '14 at 10:39

0

(int) -2 = 0xfffffffe

(int) 10 = 0x0000000a                                  

0xfffffffe ^ 0x0000000a = fffffff4 = (int) -12

edited Apr 26 '14 at 10:39

Gwenc37

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answered Apr 26 '14 at 10:15

hasan

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When answering using code fragment please describe what it does and how it fixes the problems. – Tomasz Kowalczyk Apr 26 '14 at 11:14

Bitwise addition of opposite signs

4 Answers4