Binary

Binary problems are quite rare in interviews and even online assessments but it's always good to know

Corner cases

1. Check for overflow/underflow

2. Negative numbers (they use the twos complement system)

XOR behavior

The XOR (^) operator is quite commonly used to solve binary problems, these are some important properties you should familiarize yourself with:

1. n ^ n = 0

2. n ^ m == m ^ n

3. n ^ (m ^ k) == (n ^ m) ^ k

4. n ^ 0 = n

Common bitmasks

Bitmasks are commonly used to "force" a certain set of bits to be used. They are also used to constraint Python's numbers as Python doesn't use 32 bits for integers so using a manual bitmask is necessary for constraining it

1. Retrieving the upper 16 bits: 0xffff0000

2. Retrieving the lower 16 bits: 0x0000ffff

3. Retrieving all bits in groups of 4: 0xff00ff00

4. Retrieving all bits in groups of 2: 0xcccccccc

5. Retrieving all single bits: 0xaaaaaaaa

Techniques

1. Test is bit K is set: num & (1 << k) != 0

2. Set bit K: num |= (1 << k)

3. Turn off bit K: num &= ~(1 << k)

4. Toggle bit K: num ^= (1 << k)

5. Multiply by $2^K$: num << k

6. Divide by $2^K$: num >> k

7. Check if number is power of 2: (num & num - 1) == 0 or num & (-num) == num

8. Remove rightmost set bit: num & (num - 1)

9. Swapping two variables (only positive numbers): num1 ^= num2; num2 ^= num1; num1 ^= num2

For more information and tricks, refer to this post.