Bitwise XNOR Calculator
Calculate bitwise XNOR between two binary, hexadecimal or unsigned decimal values. Compare matching bit positions, inspect the XOR intermediate value and calculate the exact fixed-width XNOR result for 8, 16, 32 or 64-bit integers.
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Bitwise XNOR Calculator
The Bitwise XNOR Calculator compares two fixed-width integers one bit at a time and returns 1 wherever the two corresponding bits are identical. It returns 0 wherever those bits are different.
XNOR is the complement of XOR, which is why it is sometimes called the equivalence operation. You can enter binary, hexadecimal or unsigned decimal values and calculate exact 8-bit, 16-bit, 32-bit or 64-bit results.
The calculator also displays the intermediate XOR value, hexadecimal and decimal outputs, matching-bit count and a position-by-position comparison.
How to Calculate Bitwise XNOR
Enter values A and B, choose their number format and select a bit width. The calculator aligns both values to that width, calculates XOR and then inverts every XOR bit inside the selected width.
A:
11001100
B:
10101010
A XOR B:
01100110
Invert XOR:
10011001
XNOR:
10011001
Hex:
99
Decimal:
153Bitwise XNOR Formula
XNOR can be expressed as the complement of XOR. For a fixed-width unsigned value, the complement must be restricted to the chosen number of bits.
XNOR(A, B) = NOT(A XOR B)
For width w:
mask = 2^w - 1
XNOR = mask XOR (A XOR B)The width mask ensures that only the intended 8, 16, 32 or 64 bits are inverted.
XNOR Truth Table
XNOR produces 1 whenever both input bits are the same. This includes both 0,0 and 1,1.
| A | B | A XOR B | A XNOR B |
|---|---|---|---|
| 0 | 0 | 0 | 1 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 1 |
Binary XNOR Example
A:
11110000
B:
10101010
XOR:
01011010
XNOR:
10100101
Hex:
A5
Decimal:
165Every XNOR bit indicates whether the corresponding A and B positions match.
Hexadecimal XNOR Example
Hexadecimal input is expanded into a fixed-width binary value before XNOR is applied.
A:
0xCC
B:
0xAA
Binary:
CC = 11001100
AA = 10101010
XOR:
66
XNOR:
99Therefore, 8-bit hexadecimal CC XNOR AA equals hexadecimal 99.
Decimal XNOR Example
A:
204
B:
170
8-bit:
204 = 11001100
170 = 10101010
XNOR:
10011001
Decimal:
153Decimal values are interpreted as unsigned integers and padded to the selected width before the calculation.
Why XNOR Detects Matching Bits
XOR marks differences: XOR returns 1 when two bits differ. XNOR inverts that result, so it marks similarities instead.
A:
10110100
B:
11100100
Compare:
1 = 1 → XNOR 1
0 ≠ 1 → XNOR 0
1 = 1 → XNOR 1
1 ≠ 0 → XNOR 0
0 = 0 → XNOR 1
1 = 1 → XNOR 1
0 = 0 → XNOR 1
0 = 0 → XNOR 1For this reason, bitwise XNOR can be viewed as a bit-by-bit equality mask.
XNOR of Identical Values
If A and B are identical, XOR is zero in every position. Inverting that zero result produces all ones.
8-bit:
A:
10100101
B:
10100101
XOR:
00000000
XNOR:
11111111
Hex:
FFTherefore an all-ones XNOR result means every compared bit matched.
XNOR of Opposite Bit Patterns
When every bit of one value is the opposite of the corresponding bit in the other value, XOR produces all ones and XNOR produces all zeros.
A:
10101010
B:
01010101
XOR:
11111111
XNOR:
00000000Why Bit Width Matters for XNOR
XNOR includes a NOT operation, so the result depends on the number of bits being considered.
A = 1
B = 1
8-bit:
00000001
00000001
--------
XNOR
11111111
= 255
16-bit:
0000000000000001
0000000000000001
----------------
XNOR
1111111111111111
= 65535The inputs are numerically identical, but a wider result contains more matching leading-zero positions.
8-Bit XNOR Calculator
An 8-bit XNOR compares exactly eight positions and produces a result from 00 to FF hexadecimal.
A:
00001111
B:
00111100
XOR:
00110011
XNOR:
11001100
Hex:
CC
Decimal:
20416-Bit XNOR Calculator
For 16-bit calculations, both inputs are expanded to sixteen binary positions before XOR and inversion.
A:
0x1234
B:
0x00FF
XOR:
0x12CB
16-bit XNOR:
0xED3432-Bit XNOR Calculator
The tool handles the full unsigned 32-bit range without relying on ordinary signed JavaScript 32-bit bitwise output.
A:
0xFFFFFFFF
B:
0x0F0F0F0F
XOR:
0xF0F0F0F0
XNOR:
0x0F0F0F0F64-Bit XNOR Calculator
64-bit values are calculated with exact BigInt arithmetic so values larger than JavaScript’s safe floating-point integer range remain exact.
A:
0xFFFFFFFFFFFFFFFF
B:
0x0000000000000001
XOR:
0xFFFFFFFFFFFFFFFE
XNOR:
0x0000000000000001XNOR vs XOR
XNOR is the exact fixed-width complement of XOR. XOR highlights different bits, while XNOR highlights matching bits.
| Operation | 0,0 | 0,1 | 1,0 | 1,1 |
|---|---|---|---|---|
| XOR | 0 | 1 | 1 | 0 |
| XNOR | 1 | 0 | 0 | 1 |
XNOR vs NAND
XNOR and NAND are different inverted logic operations. XNOR inverts XOR, while NAND inverts AND.
For A=1 and B=0:
XOR:
1
XNOR:
0
AND:
0
NAND:
1XNOR is primarily an equality operation, while NAND is false only when both inputs are one.
XNOR as a Bit Equality Mask
A multi-bit XNOR result can be interpreted as an equality mask. Every 1 marks a matching input position, and every 0 marks a difference.
A:
11001010
B:
11000011
XNOR:
11110110
1 = corresponding bits match
0 = corresponding bits differCounting the one bits in the XNOR result therefore tells you how many bit positions match.
XNOR and Hamming Distance
Hamming distance counts the number of positions at which two equal-width bit strings differ. XOR naturally marks those differing positions with ones, while XNOR marks the matching positions.
Width:
8 bits
XNOR ones:
6
Matching positions:
6
Different positions:
8 - 6 = 2
Hamming distance:
2The calculator reports matching and different bit counts directly for this reason.
Bitwise XNOR in Programming
Many languages do not provide a dedicated XNOR operator. It can be constructed by XORing the values and then inverting the result inside a defined width.
Concept:
xnor = NOT (A XOR B)
8-bit fixed width:
mask = 0xFF
xnor = mask XOR (A XOR B)The mask prevents the NOT operation from extending beyond the intended number of bits.
Common Uses of Bitwise XNOR
XNOR is useful in digital electronics, equality comparison, logic gate simulation, hardware design, bit-mask analysis, error detection and computer science education.
A hardware comparator may use XNOR-style logic to determine whether two corresponding bits are equal. Multi-bit equality can then be checked by testing whether all XNOR output bits are one.
Typical applications
Common applications include digital comparators, Boolean logic verification, bit-pattern comparison, hardware testing, embedded programming, similarity masks and Hamming-distance analysis.
Common Bitwise XNOR Mistakes
A common mistake is calculating XOR and forgetting the final inversion. XOR produces ones where bits differ; XNOR must invert those positions.
Another mistake is ignoring bit width. Since XNOR involves NOT, leading zero positions also become matching ones when both values have leading zeros.
It is also important not to treat XNOR as ordinary numeric equality. Numeric equality returns a single true or false result, while bitwise XNOR produces one result bit for every compared position.
Bitwise XNOR Calculator Limitations and Notes
The calculator treats decimal values as unsigned integers. Negative input is not accepted because the binary representation of negative values depends on a signed format and width.
Input must fit within the selected 8, 16, 32 or 64-bit width. Shorter values are effectively padded with leading zeros before comparison.
The final XNOR value is explicitly masked to the selected width, ensuring that the output remains a fixed-width unsigned integer.