🔢 NOR Calculator
Perform bitwise NOR operations on binary numbers
How to Use This Calculator
Enter Binary Numbers
Input two binary numbers in the input fields. The calculator accepts only 0s and 1s. Examples: 1010, 1100, 1111. NOR is the inverse of OR, so it returns 1 only when both inputs are 0.
Click Calculate NOR
Press the "Calculate NOR" button to perform the bitwise NOR operation. NOR is equivalent to NOT (A OR B), so it first performs OR, then inverts the result.
Review Results
The result shows both the binary NOR result and the decimal equivalent. NOR returns 1 only when both input bits are 0, making it useful for checking if both values are zero.
Formula
NOR(A, B) = NOT (A OR B)
Bitwise NOR: Result bit is 1 only if both input bits are 0
How it works:
The NOR operation is the logical inverse of OR. It first performs OR on the two binary numbers, then inverts the result. NOR returns 1 only when both input bits are 0, and 0 otherwise.
NOR Truth Table:
| A | B | A NOR B |
|---|---|---|
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 0 |
Example 1: 1010 NOR 1100
- First, compute OR: 1010 OR 1100 = 1110
- Then, invert: NOT 1110 = 0001
- Result: 0001 (binary) = 1 (decimal)
Example 2: 0000 NOR 0000
- First, compute OR: 0000 OR 0000 = 0000
- Then, invert: NOT 0000 = 1111
- Result: 1111 (binary) = 15 (decimal)
Example 3: 1111 NOR 1111
- First, compute OR: 1111 OR 1111 = 1111
- Then, invert: NOT 1111 = 0000
- Result: 0000 (binary) = 0 (decimal)
Frequently Asked Questions
What is a bitwise NOR operation?
NOR (NOT OR) is a logical operation that returns 1 only when both input bits are 0. It's the inverse of OR: NOR(A, B) = NOT (A OR B). NOR is functionally complete in digital logic, meaning all other logic gates can be constructed using only NOR gates.
Why is NOR called "functionally complete"?
NOR is functionally complete because you can construct all other logic operations (AND, OR, NOT, XOR, etc.) using only NOR gates. This property makes NOR gates fundamental in digital circuit design. Similarly, NAND gates are also functionally complete.
What's the difference between NOR and NAND?
NOR is NOT (A OR B), returning 1 only when both inputs are 0. NAND is NOT (A AND B), returning 1 except when both inputs are 1. Both are functionally complete, but they have opposite truth tables. NOR is the inverse of OR, NAND is the inverse of AND.
When is NOR operation used in programming?
NOR operations are less common in high-level programming but are important in: digital circuit design, hardware description languages, low-level bit manipulation, checking if both values are zero, and implementing complex logic gates using only NOR gates.
How does NOR relate to De Morgan's law?
De Morgan's law states that NOT (A OR B) = (NOT A) AND (NOT B). Since NOR is NOT (A OR B), we can also write NOR(A, B) = (NOT A) AND (NOT B). This shows that NOR can be constructed using AND and NOT gates.
Can I use NOR with decimal numbers?
Yes, but the calculator converts decimal numbers to binary first. The NOR operation is performed bitwise, then converted back to decimal. Enter your decimal numbers, and the calculator will show both binary and decimal representations of the NOR result.