3.1.3.5 Logic and bit operations in Python | Bit shifting

Binary left shift and binary right shift

Python offers yet another operation relating to single bits: shifting. This is applied only to integer values, and you mustn't use floats as arguments for it.

You already apply this operation very often and quite unconsciously. How do you multiply any number by ten? Take a look:

12345 × 10 = 123450

As you can see, multiplying by ten is in fact a shift of all the digits to the left and filling the resulting gap with zero.

Division by ten? Take a look:

12340 ÷ 10 = 1234

Dividing by ten is nothing but shifting the digits to the right.

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The same kind of operation is performed by the computer, but with one difference: as two is the base for binary numbers (not 10), shifting a value one bit to the left thus corresponds to multiplying it by two; respectively, shifting one bit to the right is like dividing by two (notice that the rightmost bit is lost).

The shift operators in Python are a pair of digraphs: << and >>, clearly suggesting in which direction the shift will act.

value << bits value >> bits

The left argument of these operators is an integer value whose bits are shifted. The right argument determines the size of the shift.

It shows that this operation is certainly not commutative.

The priority of these operators is very high. You'll see them in the updated table of priorities, which we'll show you at the end of this section.

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Take a look at the shifts in the editor window.

The final print() invocation produces the following output:

17 68 8

Note:

• 17 // 2 → 8 (shifting to the right by one bit is the same as integer division by two)
• 17 * 4 → 68 (shifting to the left by two bits is the same as integer multiplication by four)

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And here is the updated priority table, containing all the operators introduced so far:

Priority	Operator
1	~, +, -	unary
2	**
3	*, /, //, %
4	+, -	binary
5	<<, >>
6	<, <=, >, >=
7	==, !=
8	&
9	|
10	=, +=, -=, *=, /=, %=, &=, ^=, |=, >>=, <<=

•  Sandbox

1

2

3

4

var = 17

varRight = var >> 1

varLeft = var << 2

print(var, varLeft, varRight)

• Console