Bitwise operations work on each pair of bits independently. NOR is used for digital logic design: NOR is a universal gate from which every other gate (and the Apollo Guidance Computer) can be built. Programmers meet it in C, Java, Python and JavaScript as the ~(a | b) operator.
How to use the Bitwise NOR Calculator
- Representation
- Number format
- Number 1
- Number 2
- Operation
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
Choose the bit width (representation) and the input format, then enter both numbers. They are padded to the chosen width, combined bit by bit and the result is shown in every common base. With a fixed width, the signed value uses two’s complement.
Tips
- Choose a bit width (8, 16, 32 …) so negative numbers and overflow are shown correctly.
- Group binary digits in fours – each group is one hexadecimal digit.
- The leftmost bit is the sign bit in two’s complement.
- Everything is calculated exactly with whole-number arithmetic in your browser.
Common mistakes to avoid
- Reading a signed number as unsigned (or the reverse).
- Forgetting to add 1 when forming a two’s complement.
- Dropping leading zeros that matter for a fixed bit width.
Formula
a NOR b is 1 only when both bits are 0 – the negation of OR; truth table: 0 0 → 1, 0 1 → 0, 1 0 → 0, 1 1 → 0
Worked example
Inputs — Representation: 8-bit; Number format: Binary; Number 1: 1011; Number 2: 0110; Operation: NOR.
Results — Result (binary) = 1111 0000; Result (decimal, unsigned) = 240; Result (decimal, signed two's complement) = -16; Result (octal) = 360; Result (hexadecimal) = F0; Bit by bit = 0000 1011
NOR 0000 0110
─────────
= 1111 0000.
Key terms
- Bit
- A binary digit, 0 or 1.
- Bit mask
- A pattern of bits used to select or change other bits.
Frequently asked questions
What does bitwise NOR do?
It compares two numbers bit by bit: a NOR b is 1 only when both bits are 0 – the negation of OR.
Why choose a bit width?
Operations like NOT, NOR and the signed value depend on how many bits the number has.
Can I enter decimal numbers?
Yes – choose Decimal as the number format.
What is the difference between bitwise and logical NOR?
Logical operators treat whole values as true/false; bitwise ones act on every bit separately.
What formula does the Bitwise NOR Calculator use?
a NOR b is 1 only when both bits are 0 – the negation of OR; truth table: 0 0 → 1, 0 1 → 0, 1 0 → 0, 1 1 → 0.