If we have:

x = 1101 and y = 101

How to XORing these numbers?

  • 1
    $\begingroup$ Why would you want to XOR these numbers? $\endgroup$ Oct 23, 2015 at 7:46
  • $\begingroup$ You already asked essentially the same question on Stack Overflow: stackoverflow.com/q/31520787/781723. It would have been better to mention the comments you already got over there when you asked it here, and link to the pre-existing question on Stack Overflow in this post. $\endgroup$
    – D.W.
    Oct 10, 2016 at 3:25

3 Answers 3


There are multiple ways to interpret this XOR.

The most common one is that you XOR bit-wise, and that these strings represent numbers, so adding 0 to the left doesn't change their value.

Then $5 \equiv 101 \to 0101$ and then you XOR bit-wise.

x 1101
y 0101
------- XOR

which gives 8, if we are talking about unsigned numbers. However, the above depends on my understanding of your system. Change the assumptions, change the results.

  • $\begingroup$ What if we have two binary numbers first one 8-bits and the second one is 55-bits. Is there another method to xorring them withot add "0"? $\endgroup$
    – SHdotCom
    Oct 23, 2015 at 12:31
  • $\begingroup$ what is the aim of XOR'ing them? $\endgroup$
    – Ran G.
    Oct 23, 2015 at 13:57

Look first you should know is your numbers in Signage system value or not if they are in Signage system value you should do some stuff 1_ your number is positive (it means the last bit is zero such as 101 this number is -3) so in this case if you want to increase the number of bits you should add 1 to last bit . in your case the number 101 turns into 1101 and 1101 xor 101 turns into 1101 xor 1101 and the answer is 0000 2_ but if your numbers were normal (not in Signage system value mode) very easy you add zero to last bit . in your case 1101 xor 101 become 1101 xor 0101 and the answer is 1000

  • $\begingroup$ XOR is a logical operation, so it doesn't make too much sense to sign-extend numbers being XORed. $\endgroup$ Apr 27, 2018 at 19:05

if x and y are integer values, then

int XOR(int x,int y)
    return x^y;

whereas, if x and y are strings, then

string XOR(string x,string y)
    auto temp= bitset<4>(x) ^ bitset<3>(y);
    string u;
    return u;
  • 2
    $\begingroup$ In the notation of your 2nd code block, the question is about bitset<4>(x) ^ bitset<3>(y). $\endgroup$
    – greybeard
    Dec 13, 2019 at 3:28

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