Bitwise XOR: 1011 0110 ^ 0110 1101 — XOR gate

coredifference mask between two bytes

Answer

11011011

Why this example is worth doing

The result marks every bit position where the two bytes differ, and counting the 1s in it gives the Hamming distance between them — the link this page makes to the coding-theory half of the site. The page also notes the self-inverse property: applying the same mask twice restores the original, which is why XOR is the operator behind both simple encryption and in-place swaps.

Try your own input in the XOR gate. Truth table, symbol and algebraic form for A ⊕ B, the difference detector.

How the answer is reached

Column by column

A10110110

B01101101

result11011011

Column by column — columns bit, A, B, result
bitABresult
7101
6011
5110
4101
3011
2110
1101
0011

Compare with

Open the XOR gate

This input is entered in the tool itself — it is too rich for a link to carry.

Note:

Notation this page assumes

  • Symbols: · is AND, + is OR, ⊕ is XOR, a prime or an overline is NOT. The field also takes ∧ ∨ ¬ ~ ! & | and the words.
  • Operator precedence, tightest first: NOT, then AND (including juxtaposition), then XOR/XNOR, then NAND/NOR, then OR, then IMPLIES, then IFF.
  • Gate symbols follow whichever standard the header toggle is set to: ANSI/IEEE Std 91-1984 distinctive shapes, or IEC 60617-12 rectangles.

Sources

  • ANSI/IEEE Std 91-1984, Graphic Symbols for Logic Functions
  • IEC 60617-12, Graphical Symbols for Diagrams — Binary Logic Elements