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Bitwise expressions#

Code Example

Runnable Example in Jac and JacLib

# Bitwise Expressions

with entry {
    # Bitwise OR
    print(5 | 3);
    print(12 | 7);

    # Bitwise XOR
    print(5 ^ 3);
    print(12 ^ 7);

    # Bitwise AND
    print(5 & 3);
    print(12 & 7);

    # Left shift
    print(5 << 1);
    print(5 << 2);

    # Right shift
    print(10 >> 1);
    print(10 >> 2);

    # Bitwise NOT (unary)
    print(~5);
    print(~0);
    print(~-1);

    # Combined bitwise operations
    print((8 | 4) & 12);
    print(5 ^ 3 & 7);

    # Chained operations
    print(15 & 7 | 8);
    print(5 << 1 >> 1);

    # Complex expression
    result = (12 | 5) & (7 ^ 3);
    print(result);
}

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# Bitwise Expressions

with entry {
    # Bitwise OR
    print(5 | 3);
    print(12 | 7);

    # Bitwise XOR
    print(5 ^ 3);
    print(12 ^ 7);

    # Bitwise AND
    print(5 & 3);
    print(12 & 7);

    # Left shift
    print(5 << 1);
    print(5 << 2);

    # Right shift
    print(10 >> 1);
    print(10 >> 2);

    # Bitwise NOT (unary)
    print(~5);
    print(~0);
    print(~-1);

    # Combined bitwise operations
    print((8 | 4) & 12);
    print(5 ^ 3 & 7);

    # Chained operations
    print(15 & 7 | 8);
    print(5 << 1 >> 1);

    # Complex expression
    result = (12 | 5) & (7 ^ 3);
    print(result);
}

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from __future__ import annotations
from jaclang.runtimelib.builtin import *
print(5 | 3)
print(12 | 7)
print(5 ^ 3)
print(12 ^ 7)
print(5 & 3)
print(12 & 7)
print(5 << 1)
print(5 << 2)
print(10 >> 1)
print(10 >> 2)
print(~5)
print(~0)
print(~-1)
print((8 | 4) & 12)
print(5 ^ 3 & 7)
print(15 & 7 | 8)
print(5 << 1 >> 1)
result = (12 | 5) & (7 ^ 3)
print(result)
Jac Grammar Snippet 
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bitwise_or: (bitwise_or BW_OR)? bitwise_xor
bitwise_xor: (bitwise_xor BW_XOR)? bitwise_and
bitwise_and: (bitwise_and BW_AND)? shift
shift: (shift (RSHIFT | LSHIFT))? logical_or

Description

Bitwise expressions manipulate individual bits in integer values using logical operations and shift operators.

Bitwise OR Operator

Lines 5-6 demonstrate the bitwise OR operator |. The OR operation compares each bit position:

Operation Binary Decimal
5 0101 5
3 0011 3
5 | 3 0111 7

Each bit is 1 if either operand has 1 in that position. Line 5 produces 7 because all positions with 1 in either number result in 1.

Bitwise XOR Operator

Lines 9-10 show the bitwise XOR (exclusive OR) operator ^. XOR returns 1 only when bits differ:

Operation Binary Decimal
5 0101 5
3 0011 3
5 ^ 3 0110 6

Line 9 produces 6. The rightmost bit is 0 (both operands have 1), but the second bit from right is 1 (5 has 0, 3 has 1).

Bitwise AND Operator

Lines 13-14 demonstrate the bitwise AND operator &. AND returns 1 only when both operands have 1:

Operation Binary Decimal
5 0101 5
3 0011 3
5 & 3 0001 1

Line 13 produces 1 because only the rightmost bit is 1 in both numbers.

Left Shift Operator

Lines 17-18 show the left shift operator <<. Left shift moves all bits to the left, filling with zeros:

graph LR
    A[5 = 0101] -->|<< 1| B[1010 = 10]
    A -->|<< 2| C[10100 = 20]
Operation Binary Decimal Equivalent
5 0101 5 5
5 << 1 1010 10 5 * 2
5 << 2 10100 20 5 * 4

Left shifting by n positions multiplies by 2^n.

Right Shift Operator

Lines 21-22 demonstrate the right shift operator >>. Right shift moves all bits to the right:

Operation Binary Decimal Equivalent
10 1010 10 10
10 >> 1 0101 5 10 / 2
10 >> 2 0010 2 10 / 4

Right shifting by n positions divides by 2^n (integer division).

Bitwise NOT Operator

Lines 25-27 show the bitwise NOT operator ~ (unary). NOT inverts all bits. Due to two's complement representation:

graph LR
    A[~x] --> B[Result: -x + 1]
Value Result Explanation
~5 -6 -(5 + 1)
~0 -1 -(0 + 1)
~-1 0 -(-1 + 1)

In two's complement, ~x always equals -(x + 1).

Combined Bitwise Operations

Lines 30-31 demonstrate combining bitwise operations. Line 30 uses parentheses to control order: 1. 8 | 4 = 12 (binary: 1000 | 0100 = 1100) 2. 12 & 12 = 12 (binary: 1100 & 1100 = 1100)

Line 31 follows operator precedence (AND before XOR): 1. 3 & 7 = 3 (binary: 0011 & 0111 = 0011) 2. 5 ^ 3 = 6 (binary: 0101 ^ 0011 = 0110)

Chained Bitwise Operations

Lines 34-35 show chaining operators. Line 34: AND has higher precedence than OR: 1. 15 & 7 = 7 (binary: 1111 & 0111 = 0111) 2. 7 | 8 = 15 (binary: 0111 | 1000 = 1111)

Line 35: Shifts have equal precedence, evaluated left-to-right: 1. 5 << 1 = 10 (double: 0101 → 1010) 2. 10 >> 1 = 5 (halve: 1010 → 0101)

Complex Bitwise Expression

Lines 38-39 demonstrate a complex expression. Breaking it down:

graph TD
    A[12 | 5] --> B[13: 1101]
    C[7 ^ 3] --> D[4: 0100]
    B --> E[13 & 4]
    D --> E
    E --> F[4: 0100]
  1. 12 | 5 = 13 (binary: 1100 | 0101 = 1101)
  2. 7 ^ 3 = 4 (binary: 0111 ^ 0011 = 0100)
  3. 13 & 4 = 4 (binary: 1101 & 0100 = 0100)

Bitwise Operator Precedence

From highest to lowest precedence: 1. ~ (NOT) - unary operator 2. <<, >> (shifts) 3. & (AND) 4. ^ (XOR) 5. | (OR)

Common Uses for Bitwise Operations

  • Flags and permissions (checking/setting individual bits)
  • Optimization (multiplication/division by powers of 2)
  • Cryptography and hashing
  • Low-level hardware control
  • Data compression
  • Network protocol parsing