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• Bitwise Operators
  • Topics
  • Operators
    • Logical AND & operator
    • Logical OR | operator
    • Logical NOT ~ operator
    • Logical XOR ^ operator
    • Logical LSHIFT << operator
    • Logical RSHIFT >> operator
  • Using Bitwise Operators
    • Quick Multiplication / Division
    • Test, Set, Clear
    • XOR Invertibility
• Powerpoint

Bitwise Operators

Topics

• Bitwise Operators
  • Topics
  • Operators
    • Logical AND & operator
    • Logical OR | operator
    • Logical NOT ~ operator
    • Logical XOR ^ operator
    • Logical LSHIFT << operator
    • Logical RSHIFT >> operator
  • Using Bitwise Operators
    • Quick Multiplication / Division
    • Test, Set, Clear
    • XOR Invertibility
• Powerpoint

Operators

• CPUs only allow us to manipulates BYTES, not BITS
• Cannot directly manipulate bits
• How do we manipulate bits?
  • Bitwise operators
    • Means “at-the-bit-level”

Logical AND & operator

• Logical AND is a binary operator. Is signed agnostic.
• Algorithm: line up bits. Where the column has two 1s, the result is 1. Otherwise, it is 0.

  0b0110_0110
& 0b0100_0100
-------------
  0b0100_0100

Logical OR | operator

• Logical OR is a binary operator. Is signed agnostic.
• Algorithm: line up bits. Where a column has at least a 1, the result is 1. Otherwise, it is 0.

  0b0110_0110
| 0b0100_0101
-------------
  0b0110_0111

Logical NOT ~ operator

• Logical NOT is a unary operator. Is signed agnostic. Also called “one’s complement”
• Algorithm: flip all 0s to 1s and all 1s to 0s.

~0b0110_0110 = 0b1001_1001

Logical XOR ^ operator

• Logical XOR (exclusive OR) is a binary operator. Is signed agnostic.
• Algorithm: line up bits. Where the column has exactly one 1, the result is 1. Otherwise, it is 0.

  0b0110_0110
^ 0b0100_0101
-------------
  0b0010_0011

Logical LSHIFT << operator

• Logical LSHIFT (left shift) is a binary operator. Is signed agnostic.
• value « number_of_shifts
  • Bits that fall off the left are discarded
  • 0s are added from the right
  • Mathematically: value * 2^{number_of_shifts}

0b0100_1001 << 2 = 0b0010_0100

Logical RSHIFT >> operator

• Logical RSHIFT (right shift) is a binary operator. Is signed agnostic.
• unsigned_value » number_of_shifts
  • Bits that fall off the right are discarded
  • 0s are added from the left
  • Mathematically: unsigned_value / 2^{number_of_shifts}

0b0100_1001 >> 2 = 0b0001_0010

Using Bitwise Operators

Quick Multiplication / Division

Left

• a « 1 is the same as a * 2
• a « 2 is the same as a * 4
• a « 3 is the same as a * 8

Right

• a » 1 is the same as a / 2
• a » 2 is the same as a / 4
• a » 3 is the same as a / 8

Test, Set, Clear

• Test – Check to see if a single bit is 0 or 1
• Set – Set a single bit to 1
• Clear – Clear a single bit to 0

XOR Invertibility

• XOR is an inversion of itself. Used in cryptography for “stream ciphers”.

Powerpoint

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