Bitwise Operators

• Integers (int and long) can be considered as collections of 32 or 64 bits.
• Bitwise operators perform logical operations on each bit position, where 1 is regarded as true and zero false.
• Bitwise and (a & b) - Result is 1 in every bit position where both operands have a 1.
• Bitwise or (a | b) - Result is 1 only in positions where one or both operands have a 1.
• Bitwise xor (a ^ b)- Result is 1 in positions where the two corresponding bits are different.
• Bitwise not (~a) - Unary operator. Result is each bit of operand inverted.
• Shift left (a << n) - Shifts bits n positions left. Zeros added on right.
• Shift right (a >> n) - Shifts bits n positions right. High-order bit inserted on left.
• Shift right (a >>> n) - Shifts bits n positions right. Zeros inserted at left.
• See Deitel&Deitel p 1117

Bitwise Operators - Exercises

• For the following examples, note that 3 is 0000...0011, 5 is 0000...0101, and -1 is 1111...1111.
• 3 & 5 ____________________
• 3 | 5 ____________________
• 3 ^ 5 ____________________
• ~3 ____________________
• 5 << 2 ____________________
• 5 >> 2 ____________________
• -1 >> 30 ____________________
• -1 >>> 30 ____________________

Bitwise Operators - Uses

• Efficient storage.
  • Status bits. Eg, Mouse event key mask.
  • Eg, representing Connect-Four board.
  • Packing or unpacking values into a single int/long.
• Efficient computation
  • On some (esp old) machines, shifting is faster than multiplying or dividing by powers of two.
• Problems
  • How could you use bit operations to test whether a number is odd?
  • How would you multiply by 256?

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