Why is 1 << 3 equal to 8 and not 6?

2018-06-03 18:00:04

This question already has an answer here:

What are bitwise shift (bit-shift) operators and how do they work? 8 answers

Shifting a number to the left is equivalent to multiplying that number by 2n where n is the distance you shifted that number.

To see how is that true lets take an example, suppose we have the number 5 so we shift it 2 places to the left, 5 in binary is 00000101 ie

0×27 + 0×26 + 0×25 + 0×24 + 0×23 + 1×22 + 0×21 + 1×20 = 1×22 + 1×20 = 4 + 1 = 5

now, 5 << 2 would be 00010100 ie

0×27 + 0×26 + 0×25 + 1×24 + 0×23 + 1×22 + 0×21 + 0×20 = 1×24 + 1×22 = 16 + 4 = 20

But we can write 1×24 + 1×22 as

1×24 + 1×22 = (1×22 + 1×20)×22 = 5×4 → 20

and from this, it is possible to conclude that 5 << 2 is equivalent to 5×22, it would be possible to demonstrate that in general

k << m = k×2m

So in your case 1 << 3 is equivalent to 23 = 8, since

1 << 3 → b00000001 << 3 → b00001000 → 23 -> 8

If you instead did this 3 << 1 then

3 << 1 → b00000011 << 1 → b00000110 → 22 + 21 → 4 + 2 → 6

1 in binary is 0000 0001

by shifting to left by 3 bits (ie 1 << 3 ) you get

0000 1000

Which is 8 in decimal and not 6.

因为两个三的力量是八。

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