0b0101_0101 & 0b0001_1100 → 0b0001_0100

& logical AND is a logical carryless bitwise multiply, used for masking (getting rid of parts of a word you don’t want), 1s where both operands have a 1 otherwise 0. Don’t confuse this with &&.

0 & 0 → 0
0 & 1 → 0
1 & 0 → 0
1 & 1 → 1

& Tips

• Given that you have a mask to describe the bit (all zeros, one one), to turn off a bit, use & ~mask .
• A quick way to determine if n is odd is to use the expression (n&1) != 0.
• (n & -n) is the highest power of two that is a divisor of n. It finds the rightmost one bit and isolates it.
• A quick way to calculate the remainder modulo 16 is (n&15). The n &(m-1) trick works for any power of 2. If any negative numbers are involved you will get different answers from Java’s %, but possibly still useful ones.
• You can use & to quickly determine if a number is a power of two:

  boolean isPowerOfTwo = (n & -n) == n;

• To do the inverse, compute how many bits wide a number is,
  widthInBits
• Normally you create masks with hex literals, e.g. 0x007f. To dynamically create a mask with n low order 1’s, use (1<<n)-1. Beware, for int this will not work for n=32 since shifts are done modulo 32.