OR Calculator

How to use the Bitwise OR Calculator

What this calculator does

This calculator applies an inclusive bitwise OR to two fixed-width integer bit patterns. It aligns the inputs on the right, pads shorter positive patterns with leading zeros, and compares corresponding bits. Each result bit becomes 1 when the matching bit in Number 1, Number 2, or both is 1; it becomes 0 only when both input bits are 0. The calculator then reports the same result in binary, octal, and decimal notation. It is designed for checking masks, flags, register values, permissions, and introductory digital-logic exercises. It does not simulate electrical timing, overflow behavior in a particular processor, or a programming language's implicit type conversions.

When to use it

Use the calculator when you need to combine two flag sets, confirm a hand-worked logic-gate exercise, inspect a fixed-width register, or convert the result of an OR operation between common numeral systems. A bitwise OR is especially useful for enabling selected option bits without clearing bits that are already enabled. The MDN explanation of the bitwise OR operator gives a concise programming-oriented definition of the same per-bit rule.

How to calculate

1. The calculator opens with a complete 8-bit binary demonstration: Number 1 is 101011 and Number 2 is 11010. Its result and a validated example Excel workbook are available immediately.
2. Choose Binary representation. The preset choices are 4-bit, 8-bit, 12-bit, and 16-bit. Choose Other to reveal Custom bit width, where you can enter a whole number from 2 through 64.
3. Choose Datatype: Binary, Octal, or Decimal. Both number fields use the same notation. Replace the demonstration values with your own inputs; results update live.
4. Read the Binary result first, then use Octal result, Decimal result, Signed interpretation, Set bits, and the Bit-by-bit detail table to verify the operation.
5. Select Download Excel to export the current validated controls, outputs, and detail rows to a real XLSX workbook. Reset clears the demonstration values and calculated content. Because the cleared state has no complete operands, Reset also disables Download Excel until you enter a complete valid pair again.

Input guide

Binary representation is required and controls the exact word width. A wider word adds leading zero positions and permits larger patterns. For example, 8-bit supports eight binary digits. Choosing too few bits for an operand produces a validation message rather than silently truncating data. Custom bit width is required only when Other is selected; it accepts an ungrouped whole number from 2 to 64, such as 24. Decimal points, signs, spaces, and scientific notation are rejected.

Datatype is required. Binary accepts only 0 and 1, such as 101011. Octal accepts digits 0 through 7, such as 53. Decimal accepts an optional leading minus sign and base-10 digits, such as -21 or 59. Do not paste prefixes such as 0b or 0o, separators, commas, or decimal fractions. Binary and octal unsigned entries are treated as literal bit patterns within the selected width. A leading minus sign in any notation means a negative magnitude encoded with one's complement. Decimal entries use the signed one's-complement range from – (2^(n – 1) – 1) through +(2^(n – 1) – 1).

Number 1 and Number 2 are both required operands. Their order does not change the answer because OR is commutative. Higher values do not necessarily create a proportionally higher result; the decisive factor is which bit positions contain 1. A common mistake is to treat OR as ordinary addition. OR has no carry: 1 OR 1 remains 1.

Output guide

Binary result is the exact fixed-width output, grouped into four-bit blocks for readability. Leading zeros are significant to the selected word size even though they do not change the numeric value. Octal result is the same unsigned pattern converted to base 8. Decimal result is the unsigned magnitude of the pattern. Signed interpretation reads the same bits as a one's-complement signed integer; it becomes negative when the most significant bit is 1, except that the all-ones negative-zero pattern is displayed as 0. Set bits counts the 1s in the result and is useful for checking how many flags or positions are active.

The Bit-by-bit detail table is an exact identity, not an estimate. Bit position counts from the least significant bit at position 0. Place value is 2 raised to that position. Number 1 bit and Number 2 bit show the aligned inputs, and OR bit applies the inclusive truth rule. A zero row means neither input activates that position; a one row means at least one input does.

Worked example

With the startup values, the 8-bit padded operands are 0010 1011 and 0001 1010. Comparing from right to left gives 1∨0=1, 1∨1=1, 0∨0=0, 1∨1=1, 0∨1=1, 1∨0=1, 0∨0=0, and 0∨0=0. Reading the output from the most significant bit produces 0011 1011. Its active place values are 32 + 16 + 8 + 2 + 1, so the Decimal result is 59; the Octal result is 73; and Set bits is 5. These values match the first-open controls, the detail table, and the exported workbook.

Understanding inclusive OR

The word “inclusive” distinguishes OR from exclusive OR: when both inputs are 1, inclusive OR still returns 1. MDN's bitwise flags glossary shows how OR combines independent option bits in a practical programming context, while the digital signals and gates lesson from All About Circuits explains how truth tables describe logic-gate behavior. For fixed-width negative values, this calculator uses one's complement so the visible bit pattern remains central to the calculation.