bit manipulation: clearing range of bits

Question

I\'m preparing for an interview using the text, \"Cracking the Coding Interview\" by Gayle Laakman McDowell. On the section covering bit manipulation, there are two function

Answer 1

For the first question:

lets say i = 5

(1 << i )    = 0010 0000 = 32 in base 10
(1 << i ) -1 = 0001 1111 = 31 

So a & with this mask clears the most significant bit down to i because all bit positions above and including index i will be 0 and any bellow will be 1.

For the second question:

Again lets say i = 5

  (1 << (i + 1))      = 0100 0000 = 64 in base 10
  (1 << (i + 1)) - 1  = 0011 1111 = 63
~((1 << (i + 1)) - 1) = 1100 0000 = 192

So a & with this masks clears bits up to index i