How do binary operations with XOR in python work?

Question

I have the following problem with the xor operator (^) in python. I have two binary numbers, let a = 10100111 and b = 10000000. When I use the xor operator,

print (10000000 ^ 10100111)

I get the result of 166671 instead of 00100111. However, when I use

print (100 ^ 101)

I get the appropriate result in binary of 1 (001). Even if I use

print int(a) ^ int(b)

I still get the result of 166671.

Questions:

Why do I get the result of 166671 instead of the binary result of 00100111?
Why do I get the appropriate result when I use 100^101?

I am running Python version 2.7.2.

Aside: this isn't related to your issue here, but one thing that often surprises people in Python 2 is that 010 isn't either 10 (read in decimal) or 2 (read in binary), it's 8. The 0 prefix, without a b, means "read this number as octal, i.e. base 8". Just a heads-up. — DSM
– DSM, Commented Oct 8, 2013 at 16:47

falsetru · Accepted Answer · 2013-10-08 16:06:35Z

3

100 is decimal 100 (1100100 in binary). Use 0bnnn form for binary representation.

>>> 0b100
4
>>> 100
100
>>> 0b100 == 100
False

>>> 0b100 ^ 0b101
1

>>> 0b100 & 0b101
4
>>> bin(0b100 & 0b101)
'0b100'
>>> '{:b}'.format(0b100 & 0b101)
'100'

edited Oct 8, 2013 at 16:06

answered Oct 8, 2013 at 15:58

falsetru

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2 Comments

Akhil Nadh PC Over a year ago

please tell solution for python 3.x , say x=100 and y=101 x^y

falsetru Over a year ago

@AkhilNadhPC, bin(0b100 ^ 0b101) works in Python 3.

A.E. Drew · Accepted Answer · 2013-10-08 16:05:21Z

2

You are using decimal number representations, not binary.

10000000^10100111

in binary is

0b100110001001011010000000 ^ 0b100110100001110110001111

which equals

0b101000101100001111

or in decimal,

100 ^ 101

in binary is

0b1100100 ^ 0b1100101

which is

0b1

or, in decimal (which happens to be the same as in binary in this case),

answered Oct 8, 2013 at 16:05

A.E. Drew

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