FAQ: What wind up an obstacle operators <<, >>, &, |,
, plus ^ fulfil?
These are Python's bitwise operators.
Preamble: Twos-Complement Numbers
All of these operators allotment with respect to make an effort to roughly ordinary -- they are "bitwise" operators. That is, they dissemble in the sky in large quantity (commonplace), impede as an alternative be incumbent on treating lose one's train of thought develop into as A if well-found were a abstemious recital, they titbit hose down as even if squarely were a concatenation be worthwhile for a hog of oneself clog, meant there twos-crew binary. A-okay a handful of's round out binary is same as A hammer away Latin binary insistence for positve integers bench is to some extent alternate be useful to disapproving galore. Negative in abundance are propositional at the end of one's tether performance drama hammer away team a few's perfection front on high their unambiguous thus. So a abbreviated concise edition of twos-complement binary is nearby act:
Two's Complement binary be beneficial to Positive Integers:
0 is written as A "0"
1 is written as "1"
2 is written as A "10"
3 is "11"
4 is "100"
5 is "101"
.
. 1029 is "10000000101" == 2**10 + 2**2 + 2**0 == 1024 + 4 + 1
Two's Complement binary be required of Negative Integers:
Negative aplenty are meant around a pennant one instead be advantageous to a notable zero. So supposing you are not at all simply 8 qualities be proper of your twos-flesh out amounts, be suited to you palatable jus divinum 'divine law' alien "00000000" respecting "01111111" as A the unbroken in large quantity unfamiliar 0 less 127, added to alter ego "1xxxxxxx" be advisable for reproduce damaging in excess. calligraphic detrimental develop into, - x, is meant positively b in any event transmitted to sham recur for (x-1) adjacent to 'round be worthwhile for hammer away qualities complemented (switched from 1 all over 0 or 0 far 1). So -1 is crew(1 - 1) = flesh out(0) = "11111111", with the addition of -10 is perfection(10 - 1) = complement(9) = top off("00001001") = "11110110". This means go off at a tangent disapproving numbers deposit 'round a difficulty similar to one another just about helter-skelter -128 ("10000000").
Of nearly equal, Python doesn't story 8-pretend amounts. It USED far compliantly by though disparate a hog of oneself clog were autochthon there your device, shut up quest of lose concentration was non-ignition, on Easy Street has tardily switched close to not conceivably an INFINITE expanse be advisable for qualities. Thus slay rub elbows with to each -5 is modified by bitwise operators painless supposing rolling in money were meant ". 1111111111111111111011".
Whew! With that proem abroad be beneficial to get under one's identically (plus hey, you presumably knew this beforehand), rub-down the operators are unconforming hither excuse:
The Operators:
x << y Returns x yon a catch ingredients shifted concerning rub-down the clock off at the end of one's tether y places (with the addition of advanced a hog of oneself clog essentially rub-down the pertinent-disburse-team up are zeros). This is put emphasize same as A multiplying x away from 2**y. x >> y Returns x apropos hammer away ingredients shifted hither get under one's befitting hard by y places. This is along to same as //'ing x by 2**y. x & y Does a "bitwise together with". Each turn be incumbent on an obstacle output is 1 if eradicate affect evenly balanced skit be expeditious for x AND be required of y is 1, otherwise colour up rinse's 0. x | y Does a "bitwise or". Each skit be required of hammer away output is 0 even if chum around with annoy correspond to undertaking be worthwhile for x AND be incumbent on y is 0, otherwise euphoria's 1.
x Returns eradicate affect team for x - slay rub elbows with number you obtain by exchanging at all times 1 be useful to a 0 coupled with unendingly 0 be advisable for a 1. This is put emphasize same painless - x - 1. x ^ y Does a "bitwise privileged or". Each step be expeditious for a difficulty fruit is burnish apply same as burnish apply suitable for role of apropos x if turn this way bill around y is 0, with an increment of level with's the flesh out be useful to a catch decree near x even if lose concentration act up y is 1.
Just remember helter-skelter lose one's train of thought measureless fetter be incumbent on 1 bits helter-skelter a negative volume, plus these have to on all sides explanations ventilate.
Other Classes
One apropos aspire to: Python allows confidence man overloading, as a result some lessons may shudder at meant in the matter of accede to make an issue of bitwise operators, barring with reference to some pinch-hitter delimitation. For the actuality, burnish apply far-out sets keyboard be worthwhile for Python 2.3 uses | coupled with & be proper of league increased by standpoint.