Nor Calculator - Bitwise NOR, Truth Table, and Result

A nor calculator returns the bitwise NOR of two numbers by inverting the OR of each pair of corresponding bits. Type the operands in binary, octal, decimal, or hex, pick a bit width, and the result panel shows the NOR in the same base, padded in binary, and written in hex. Every position where both inputs are 0 becomes 1, and every other position becomes 0.

• • Universal logic-gate design: Build any Boolean function from a single gate type, since NOR (like NAND) is functionally complete on its own.
• • Hardware register clearing: Combine NOR with an inverter to clear bits in a control register, a common firmware pattern.
• • Digital-electronics homework and labs: Verify the 2-input NOR truth table and the 8-bit NOR output for any pair of binary inputs during coursework.
• • Bit-mask inversion in code: Generate a bit pattern with 1s wherever both inputs are 0, useful for setting all bits outside a chosen mask.

NOR is a standard bitwise operator in most languages, alongside AND, OR, XOR, and NOT. It operates one bit at a time, so the result depends on the binary representation of the inputs.

When you need the other half of the comparison, the and Calculator returns the bitwise AND of the same pair of numbers with the same base and bit-width controls.

The calculator parses the two inputs in the chosen base, masks each to the bit width, performs a bitwise OR, inverts every bit, and formats the result. The truth table card above lists the four fixed (A, B) bit pairs that drive every column of a longer NOR.

• A_bit_i: The bit at position i in the binary representation of Number 1, counted from the right starting at 0.
• B_bit_i: The bit at position i in the binary representation of Number 2, counted from the right starting at 0.
• result_bit_i: The bit at position i of the NOR result. Equals 1 only when both A_bit_i and B_bit_i are 0; otherwise 0.
• bitWidth: The chosen number of bits (4, 8, 12, or 16). Inputs and the result are masked to this width so the high bits are dropped.

According to Omni Calculator, the NOR gate performs a bit operation for each pair of bits in the inputs and produces 1 only when both input bits are 0, otherwise producing 0.

According to MDN Web Docs, the bitwise NOT operator (~) inverts every bit of its operand and is the complement used to build NOR from a bitwise OR.

To convert the inputs or the result between binary, octal, decimal, and hex without doing the math by hand, the Binary Converter accepts a value in any of those bases.

Four short ideas explain why the NOR behaves the way it does. Once these are clear, NOR stops looking like a magic operator and starts looking like an OR followed by a column-by-column bit flip.

The same rule extends to more than two inputs. A 3-input NOR returns 1 only when all three bits at that position are 0, so a single 1 anywhere in the input collapses the entire column to 0.

When the inputs are Boolean expressions with AND, OR, and NOT, the Boolean Algebra Calculator evaluates the full expression and shows the truth table for the variables.

Enter the two operands, pick the base they are written in, and pick the bit width. The result panel updates in real time.

1. 1 Type Number 1 and Number 2: Enter the two operands in the first row using the same base. Decimal takes digits, binary takes 0 and 1, and hex takes 0-9 and the letters A-F in either case.
2. 2 Pick the input base: Use the Input Base dropdown to select binary, octal, decimal, or hex. Both operands are read in this base and the result is shown in decimal, binary, and hex.
3. 3 Pick the bit width: Use the Bit Width dropdown to select 4, 8, 12, or 16. Values that would overflow a smaller width have their high bits dropped, like a fixed-width register.
4. 4 Read the NOR result: The highlighted NOR Result (Decimal) row shows the bitwise NOR as a non-negative integer. The Binary and Hex rows show the same value padded to the bit width.
5. 5 Compare against the truth table: The 2-Input NOR Truth Table card above lists the four (A, B) bit pairs and the matching output. Any column in a longer binary NOR follows one of those four rows.

Example: a digital-electronics student needs the NOR of the byte 0xF0 and the byte 0x0F. They type F0 into Number 1 and 0F into Number 2, leave the base at Hexadecimal, the bit width at 8, and read 0x0 in hex and 0 in decimal, because every column has at least one 1.

If you want AND, OR, XOR, and NOT on the same pair of numbers in a single panel, the Binary Operations Calculator runs all of the bitwise operations side by side so the results are easy to compare.

NOR is one of the simplest operators to define, but mixing bases and bit widths by hand is the easy place to lose a bit. The calculator keeps the operands, the base, and the width consistent.

• • Bit-level result without manual alignment: The result panel shows the NOR in decimal, binary, and hex at the same time, with no need to align bits on paper.
• • Works in binary, octal, decimal, and hex: Type the operands in the base your problem statement uses and the result appears in that base plus binary and hex.
• • Bit-width masking matches real hardware: Choose 4, 8, 12, or 16 bits to mimic a fixed-width register. Values that overflow the chosen width have their high bits dropped, like AND with a width-sized mask after the bitwise NOT in JavaScript or Python.
• • Truth table next to the numeric result: The 2-Input NOR Truth Table card sits beside the form, so the four (A, B) -> output rows are always one scroll away.
• • Reusable for NOR-only logic and register clearing: The same workflow works for designing NOR-only circuits, building an AND from three NOR gates, and clearing all bits outside a chosen mask.

The biggest practical win is consistency. NOR behaves the same way regardless of which base the inputs are written in, and the calculator applies that rule in one pass.

When the result is in binary and you need to read it in hex without doing the nibble grouping yourself, the Binary to Hexadecimal Calculator converts a binary string to its hexadecimal value in one step.

The bitwise NOR is fixed, but four choices about the inputs change what the result means.

• • The calculator takes exactly two operands. For three or more inputs, NOR the first two and combine the intermediate result with the next input using the same pattern.
• • The inputs are read as non-negative integers, so the result is also non-negative. For signed two's-complement integers, convert to the unsigned form first, NOR, and interpret the result as signed afterward.

When the inputs and the bit width are clear, the result is fully determined and matches what the same operation would produce in JavaScript, Python, or C.

According to Wolfram MathWorld, a NOR gate is a logic gate that implements the NOR Boolean function and is one of the two universal gates alongside NAND.

When the next step is to shift the NOR result left or right to isolate a specific group of bits, the Bit Shift Calculator performs the logical and arithmetic shifts at the same bit width.