NOR Calculator

A NOR (Not-OR) operation is a digital logic function that produces a true output (1) only if all inputs are false (0). For any other combination of inputs, the output is false (0). In terms of Boolean algebra, the NOR of two inputs A and B is written as \( \overline{A + B} \). This means the calculator first evaluates the standard logical OR of the inputs and then inverts the resulting bit. When executing bitwise NOR across multi-bit datatypes (such as 8-bit or 16-bit integers), the operation is applied independently to each corresponding pair of bits from the binary representations of Number 1 and Number 2.

Let us calculate the 4-bit bitwise NOR of Number 1 = 5 and Number 2 = 3. First, convert these decimal numbers into their 4-bit binary equivalents: Number 1 (5) becomes \( 0101_2 \) and Number 2 (3) becomes \( 0011_2 \). Next, apply the OR operation bit by bit: \( 0101 \text{ OR } 0011 = 0111 \). Finally, invert the result of the OR operation to get the NOR outcome: \( \text{NOT}(0111) = 1000_2 \). Converting the final binary result back to decimal yields \( 8_6 \) (depending on signed or unsigned datatype interpretation).

Always verify your datatype and bit limits before running operations, as a signed 8-bit integer handles negative ranges differently than an unsigned byte. Pay close attention to leading zeros in binary representations, because dropping a leading zero changes the bit length and can invert your final output in fixed-width systems.