Problem 2.68

gistfile1.txt

/*
* Mask with least signficant n bits set to 1 
* Examples: n = 6 --> 0x2F, n = 17 --> 0x1FFFF 
* Assume 1 <= n <= w
*/

int lower_one_mask(int n) { 
	/*
	 * 2ˆn-1 has bit pattern 0...01..1 (n 1’s) 
	 * But, we must avoid a shift by 32
	 */
    return (2<<(n-1)) - 1;
}

The code makes use of the trick that (1<<n)-1 creates a mask of n ones. The only challenge is to avoid shifting by w when n = w. Instead of writing 1<<n, we write 2<<(n-1). This code will not work for n = 0, but that’s not a very useful case, anyhow.