About

The bitwise OR operation compares each bit position of two binary operands: if either bit is 1, the result bit is 1. Only when both bits are 0 does the output yield 0. This operation is foundational in register-level programming, permission flag systems, and subnet mask calculations. Misapplying OR where XOR or AND is required leads to silent data corruption - flags get set that should remain clear, and bitmask filters pass values they should reject. This calculator accepts operands up to 64 bits, computes the OR using native integer arithmetic, and displays the bit-by-bit truth table so you can audit every position.

The tool outputs results simultaneously in binary, decimal, hexadecimal, and octal. It assumes unsigned integer representation. For signed interpretation, the most-significant bit would require two's complement conversion, which this tool does not perform. Pro tip: when combining Unix file permission masks (e.g., 0644 | 0111 = 0755), always verify the result against your security policy before applying chmod.

Formulas

The bitwise OR operation is defined per bit position i across two unsigned binary integers A and B:

R_i = A_i ∨ B_i

Where R_i is the result bit at position i, and ∨ is the logical disjunction. The full integer result is reconstructed as:

R = n−1∑i=0 R_i ⋅ 2ⁱ

Where n = total number of bit positions (determined by the longer operand). Equivalently, for full integers: R = A | B. Key algebraic properties of bitwise OR:

A | 0 = A (identity)

A | A = A (idempotent)

A | ¬A = 1...1 (all ones)

A | B = B | A (commutative)

Where A = first binary operand, B = second binary operand, R = result, i = bit index (LSB = 0), n = bit width.

Reference Data

A	B	A \| B	Description
0	0	0	Both bits clear → result clear
0	1	1	One bit set → result set
1	0	1	One bit set → result set
1	1	1	Both bits set → result set

Bit Width	Max Unsigned Value	Common Use	All-Ones Mask
4-bit	15	Nibble, hex digit	1111
8-bit	255	Byte, ASCII, color channel	11111111
12-bit	4095	ADC resolution, Unix permissions (octal)	111111111111
16-bit	65535	Short integer, Unicode BMP	1111111111111111
24-bit	16777215	RGB color (#FFFFFF)	111111111111111111111111
32-bit	4294967295	IPv4 address, int32	11111111111111111111111111111111
48-bit	281474976710655	MAC address	48 ones
64-bit	18446744073709551615	Long integer, memory address	64 ones

Operation	Symbol	Truth when	Identity element	Common mnemonic
AND	&	Both 1	1 (all ones)	Masking / clearing bits
OR	\|	Either 1	0	Setting / combining flags
XOR	⊕	Bits differ	0	Toggling / checksums
NOT	¬	Invert	N/A	Complement / inversion
Left Shift	<<	Multiply by 2ⁿ	0	Fast power-of-two multiply
Right Shift	>>	Divide by 2ⁿ	0	Fast power-of-two divide

Frequently Asked Questions

Bitwise OR (|) operates on each bit position independently across two integers. Logical OR (||) evaluates entire expressions as boolean true/false and short-circuits: if the left operand is truthy, the right operand is never evaluated. For example, 6 | 3 = 7 (binary 110 | 011 = 111), while 6 || 3 = 6 (returns the first truthy value). Confusing the two in C/C++ flag manipulation is a common source of bugs.

The shorter operand is implicitly zero-padded on the left (most-significant side) to match the longer operand's width. This is equivalent to treating the shorter number as having leading zeros. For instance, 101 (3-bit) OR'd with 11001 (5-bit) becomes 00101 | 11001 = 11101. This calculator performs that alignment automatically.

Because A | 0 = A for any value of A. OR-ing with 0 never sets any new bits, leaving the original value unchanged. This contrasts with AND, whose identity element is all-ones (1...1), because A & 1...1 = A.

No. Since OR only sets bits to 1 (never clears them), the result is always greater than or equal to the larger of the two operands. Formally: A | B ≥ max(A, B). This property makes OR useful for accumulating permission flags - once a flag is set, no subsequent OR operation can remove it.

In IPv4 networking, the broadcast address of a subnet is computed by OR-ing the network address with the inverted subnet mask. For example, network 192.168.1.0 with mask 255.255.255.0: the inverted mask is 0.0.0.255 (00000000.00000000.00000000.11111111 in binary). OR-ing gives broadcast address 192.168.1.255. An incorrect mask inversion leads to packets being sent to the wrong broadcast domain.

No. This calculator treats all inputs as unsigned binary integers. In two's complement, the MSB represents the sign bit, and OR-ing two negative numbers can produce unexpected positive results if you don't account for the fixed bit-width. If you need signed interpretation, first determine your target bit-width (e.g., 8, 16, 32), pad both operands to that width, then interpret the OR result's MSB as the sign bit manually.