Unitary number for “&” bitwise operator in c++

Question

I have a question, I would appreciate it if you helped me to understand it. Imagin I define the following number

c= 0x3FFFFFFF

and a = an arbitrary integer number=Q. My question is, why a &= c always is equal to "Q" and it does not change? for example, if I consider a=10 then the result of a &= c is 10 if a=256 the result of a &= c is 256. Could you please explain why? Thanks a lot.

Answer 1

Both a and c are integer types and are composed of 32 bits in a computer. The first digit of an integer in a computer is the sign bit.The first digit of a positive number is 0, and the first digit of a negative number is 1. 0x3FFFFFFF is a special value. The first two digits of this number are 0, and the other digits are all 1. 1 & 1 = 1, 1 & 0 = 0. So when the number a a is positive and less than c, a & 0x3FFFFFFF is still a itself