⚡ Free Bitwise Calculator

Binary OR Calculator

Perform a bitwise OR operation on two binary numbers instantly. BinaryCon compares matching bit positions and returns 1 whenever either input bit, or both input bits, are 1.

✓ Free ✓ Instant Result ✓ Auto Alignment ✓ Long Binary Values

A|B

Binary OR

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Binary A 0 and 1 only

Binary B 0 and 1 only

Different lengths are automatically padded with leading zeros.

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✓ OR Result

Bitwise OR result after aligning both binary values

Bit Width 0

Result 1s 0

Result 0s 0

What Is a Binary OR Calculator?

A Binary OR Calculator performs the bitwise OR operation on two binary numbers. Each pair of corresponding bits is evaluated separately.

OR returns 1 whenever at least one input bit is 1. The result becomes 0 only when both corresponding bits are 0.

1010
OR 1100
—-
1110

Inclusive OR

The standard bitwise OR operation includes the 1 OR 1 case, which also produces 1.

Bit-by-bit logic

Every corresponding position is calculated independently using the same one-bit OR truth table.

Binary OR Truth Table

A	B	A OR B
0	0	0
0	1	1
1	0	1
1	1	1

Core rule: Binary OR returns 0 only when both input bits are 0.

How to Calculate Binary OR

Write the first binary number

Enter a value containing only 0s and 1s, such as 101101.

Write the second binary number

Place the second value so corresponding binary positions can be compared.

Align the rightmost bits

If one value is shorter, add leading zeros to its left until both widths match.

Apply the OR rule

Return 1 whenever either bit or both bits are 1. Return 0 only for 0 OR 0.

Combine the output bits

Join the calculated bits from left to right to produce the final result.

Worked Example: 101101 OR 110011

Position	A	B	OR
1	1	1	1
2	0	1	1
3	1	0	1
4	1	0	1
5	0	1	1
6	1	1	1

Final result: 101101 OR 110011 = 111111

Example: 1010 OR 1100

1010
OR 1100
—-
1110

Only the rightmost bit remains 0 because that is the only position where both input bits are 0.

Binary OR with Different Bit Lengths

If the inputs have different lengths, the shorter unsigned binary number can be padded with leading zeros.

1011
0010 Then: 1011 OR 0010 = 1011

BinaryCon performs this alignment automatically while preserving the display width.

Binary OR and Decimal Values

1010₂ = 10₁₀
1100₂ = 12₁₀ Apply OR: 1010 OR 1100 = 1110 Convert the result: 1110₂ = 14₁₀ Therefore: 10 OR 12 = 14

Using OR to Set Bits

Bitwise OR is especially useful when specific bits need to be turned on without changing bits that are already set.

Original: 10010000 Mask: 00000110 OR result: 10010110

The mask turns on the selected lower bits while preserving the existing 1 bits.

Binary OR with Zero

OR with zero leaves a binary value unchanged because each bit OR 0 equals the original bit.

101101 OR 000000 = 101101

Binary OR with All Ones

OR with an all-ones pattern produces all ones at the chosen bit width.

101001 OR 111111 = 111111

Any position containing a 1 in either operand becomes 1 in the result.

Important Properties of Binary OR

Property	Formula	Meaning
Commutative	`A OR B = B OR A`	Operand order does not matter.
Associative	`(A OR B) OR C = A OR (B OR C)`	Grouping does not change the result.
Idempotent	`A OR A = A`	ORing a value with itself leaves it unchanged.
Identity	`A OR 0 = A`	An all-zero mask preserves the original bits.
All-ones rule	`A OR 111... = 111...`	Ones force corresponding output bits to 1.

Binary OR vs AND vs XOR

A	B	AND	OR	XOR
0	0	0	0	0
0	1	0	1	1
1	0	0	1	1
1	1	1	1	0

OR returns 1 when one or both input bits are 1. AND requires both bits to be 1, while XOR requires the two bits to be different.

Where Is Binary OR Used?

Setting Flags

OR can enable selected flags without clearing flags that are already active.

Permissions

Multiple permission bits can be combined into a single bit field using OR.

Embedded Systems

Control-register bits can be enabled using masks while preserving unrelated bits.

Graphics

Bit fields and packed pixel or feature values may be combined using OR operations.

Digital Logic

OR is one of the fundamental Boolean operations implemented with logic gates.

Computer Science

OR is studied alongside binary numbers, Boolean algebra, masks, gates, and low-level data structures.

Common Binary OR Mistakes

Confusing OR with XOR

1 OR 1 equals 1, while 1 XOR 1 equals 0.

Using non-binary digits

Binary values can contain only digits 0 and 1.

Incorrect bit alignment

Align values from the right and add leading zeros to the shorter value.

Confusing bitwise and logical OR

Bitwise OR works on individual bits, while logical OR normally evaluates Boolean conditions.

Related BinaryCon Tools

Binary OR Calculator FAQs

What is a binary OR operation?

Binary OR compares corresponding bits of two binary values. A result bit becomes 1 whenever either input bit or both input bits are 1.

What is 0 OR 0?

0 OR 0 = 0. This is the only OR combination that produces 0.

What is 0 OR 1?

0 OR 1 = 1.

What is 1 OR 0?

1 OR 0 = 1.

What is 1 OR 1?

1 OR 1 = 1. Standard OR is inclusive, so both inputs being 1 still produces 1.

What is 1010 OR 1100?

The result is 1110.

What is 101101 OR 110011?

The result is 111111.

What happens when a binary number is ORed with zero?

The original binary value is preserved because every bit OR 0 equals that original bit.

What happens when a value is ORed with all ones?

Every corresponding output bit becomes 1.

Why is OR useful for bitmasks?

A mask containing 1s at selected positions can turn those bits on while leaving existing 1 bits unchanged.

What is the difference between OR and XOR?

OR returns 1 for 1 OR 1, while XOR returns 0 when both bits are identical.

What is the difference between OR and AND?

OR requires at least one 1 to produce 1. AND requires both input bits to be 1.

Can binary OR use values of different lengths?

Yes. The shorter unsigned value can be left-padded with zeros before the operation.

Is binary OR commutative?

Yes. A OR B = B OR A.

Is bitwise OR the same as logical OR?

No. Bitwise OR operates on individual bits. Logical OR usually evaluates complete Boolean conditions.

Can BinaryCon process long binary OR values?

Yes. The calculator works directly with binary strings, so it can process long bit patterns without relying on ordinary floating-point conversion.

Calculate Binary OR Instantly

Use BinaryCon’s free Binary OR Calculator to compare binary values, set bits, work with masks, understand Boolean OR logic, and verify bitwise results instantly.