How does actually "&~" work?

Question

I wonder how does it work in Unix:

user$ i=5
user$ echo $((i &~ 1)) 

4

what happens inside the parentheses?

Answer 1

ok, got it

binary 5 is 101

binary 1 is 001 -> ~1 is 110

101 & 110 -> 100 which is 4 in decimals

Answer 2

Both & and ~ are bitwise operators.

• ~1 is unary bitwise negation that produces -2
• 5 & -2 is binary bitwise AND operation that produces 4