About

Low-level programming requires direct manipulation of memory bits. This functionality is essential when developing device drivers, network protocols, or optimizing embedded systems. A single bit error in a status register or a subnet mask causes system instability or security vulnerabilities. Standard calculators often fail to handle the specific constraints of fixed-width integers, such as overflow behavior in 32-bit or 64-bit architecture.

The Bitwise Calculator handles these constraints by simulating specific data types used in C, C++, Rust, and Go. It supports operations like AND, OR, XOR, NOT, and bit shifts, taking into account the sign bit for signed integers (Two's Complement representation). This tool assists developers in debugging bitmasks, setting flags, and understanding binary data structures without manual conversion errors.

Formulas

Bitwise operations manipulate the underlying binary representation of numbers. The result depends heavily on the bit-width (N) and the signedness of the integer.

Two's Complement (Signed Integers):

For a signed N-bit integer, the value x is stored such that the most significant bit (MSB) indicates the sign. If the MSB is 1, the value is negative.

Value = −b_N-1 × 2^N-1 + N-2∑i=0 b_i × 2ⁱ

Bitwise AND Truth Table:

{

0 & 0 = 00 & 1 = 01 & 0 = 01 & 1 = 1

Reference Data

Operation	Operator	Logic	Example (A=1010, B=1100)
Bitwise AND	&	1 if both bits are 1	1000
Bitwise OR	\|	1 if either bit is 1	1110
Bitwise XOR	^	1 if bits are different	0110
Bitwise NOT	~	Inverts all bits	0101 (for 4-bit)
Left Shift	<<	Shifts bits left (multiply by 2)	10100 (A << 1)
Right Shift	>>	Shifts bits right (divide by 2)	0101 (A >> 1)
Zero-fill Right Shift	>>>	Shifts right, fills with 0	Unsigned Only

Frequently Asked Questions

The binary sequence stored in memory remains identical, but the interpretation changes. In an 8-bit Signed system, the binary 11111111 represents -1. In an 8-bit Unsigned system, 11111111 represents 255. Bitwise operations like shifts can produce drastically different decimal results depending on how the Most Significant Bit (sign bit) is treated.

A Logical Right Shift (>>>) always fills the new empty bits on the left with zeros. This is useful for unsigned data. An Arithmetic Right Shift (>>) preserves the sign bit, filling the left bits with 1s if the number was negative and 0s if positive. This ensures that dividing a negative number by 2 remains negative.

Computers have fixed register sizes (8, 16, 32, 64 bits). If an operation produces a value larger than the maximum capable of being stored (e.g., shifting a 1 out of the frame), the bits are discarded (truncated). This tool simulates that behavior exactly, allowing you to see where data loss occurs in low-level casting.

Hexadecimal (base 16) aligns perfectly with binary (base 2). Every 4 bits (a nibble) maps directly to 1 hex digit (0-F). This makes reading a 32-bit or 64-bit mask significantly easier than reading a long string of binary 1s and 0s or a non-aligned decimal number.