1. Bit Manipulation

2. Binary Numbers Base 10 numbers are represented by sum of digits times powers of 10. For example: 234 = 2*10 2 +3*10 1 +4*10 0 Binary numbers are similar, except that the only digits are 1 and 0, and the digits multiply powers of 2. The string "1011" is binary for the decimal number 11. 1011 = 1*2 3 +0*2 2 +1*2 1 +1*2 0

3. Bit Operators The "and" operator: (10 & 3) = 2 Why? It's clearer expressed in binary numbers: 1010 Apply the rules for and based on each & 0011 row independently. Here 1 = True, ------ and 0 = False. Thus, 1 & 1 0010 is True and True = True = 1 The "or" operator: (10 & 3) = 11 Why? Again, clearer in binary 1010 = 10 | 0011 = 3 ------ 1011 = 11

4. Bit Operators The "xor" or "exclusive or" operator: (10 ^ 3) = 9 Why? 1010 ^ 0011 ------ 1001

5. Flags Consider a class Monster that has an integer field named traits. Traits will record capabilities of the Monster in individual bits. Bits can be defined with left shift, e.g. final static int HAS_FLYING = 1<<0; final static int HAS_INVISIBILITY = 1<<1; final static int CAN_SWIM = 1<<2; final static int FIRE_PROOF = 1<<3;

6. Flags To turn a flag on: m.traits |= CAN_SWIM; To turn a flag off: m.traits &= ~CAN_SWIM; To toggle a flag: m.traits ^= CAN_SWIM; The tilde operator "~" inverts the bits on an integer.