Why and 1 ( &1) bitwise operation always return 0 or 1

Question

I just started learning about bit wise operation and want to ask why and 1 ( &1) bitwise operation always return 0 or 1 .

Calcariferous

What do you mean by "1 ( &1) bitwise operation"? – Ette

I mean any number when and with 1 just return 0 or 1 value ( a & 1 ) – Calcariferous

What else do you expect it to return? x & 1 returns 1 if the least significant bit of x is 1 else 0. 1 & 1 = 1, 0 & 1 = 0. That's how the operator is defined. – Baroscope

Any bit except the last one is 0 because it's 0 in 1. And the last one is the same than in a. That's all. – Korikorie

Any number or just 1 and 0? – Ette

I'm voting to close this question as off-topic because it's immediately answered by any documentation on the topic – Korikorie

4 and any number will NEVER be 5 ... only 4 or 0 – Merely

Understood, thank for your help – Calcariferous

3 is little more complex with & .... you can end up with 0, 1, 2 or 3 ... with 5 you can end up with 0, 1, 4 or 5 ... with 128, only 0 or 128 ... do you need any more examples? – Merely

@Denys Séguret: I just noticed the [javascript] tag on this question. It's not even a JavaScript question lol. – Ette

Answer 1

0 & 0 === 0
0 & 1 === 0
1 & 0 === 0
1 & 1 === 1

therefore any number & 1 will always be either 0 or 1

in binary ... any number

xxxxxxxxxxxxx0

or

xxxxxxxxxxxxx1

where x can be 0 or 1

1 in binary is

00000000000001

so

xxxxxxxxxxxxx1 &
00000000000001 ==
00000000000001

xxxxxxxxxxxxx0 &
00000000000001 ==
00000000000000

Merely

Answer 2

When you perform a & 1 it will always return 0 or 1 depending upon the the last binary digit of a.

Rules:

0 & 0 = 0
0 & 1 = 0
1 & 1 = 1

For example:

a = 5 //5 = 0101
b = a & 1  = 1 //(0101 & 0001)


a = 6 //6 = 0110
b = a  & 1 = 0 //(0110 & 0001)

Hoxsie

Answer 3

This is a bitwise operation. Suppose you take 2 & 1. That would be 10 and 01 in binary. Bitwise AND will give 00. BitWise operations with 1 will give 1 or 0 always because 1 has only a significant unit's place in binary. So it cannot return any value other than a 0 or a 1.

Gwyngwyneth

Answer 4

This can be used to check if an integer is odd or even, returning a 0 for False and 1 for True.

is_odd: 1 for odd , 0 for even

odd = number & 1

is_even: 1 for even , 0 for odd

even = number & 1 ^ 1

Billie

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