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Definition & Example
 A binary word is a word with letters in the alphabet $\{0,1\}$.
the 16 Binary words of size 4  
0000  0001  0010  0011  0100  0101  0110  0111  
1000  1001  1010  1011  1100  1101  1110  1111 
 There are $2^n$ binary words of length $n$, see A000079.
Additional information
 Binary words of length $n$ are in natural correspondence with monotone lattice paths starting at $(0,0)$ and consisting of $n$ steps $(1,0)$ and $(0,1)$.
Feel free to add further combinatorial information here!
References
Sage examples
Technical information for database usage
 Binary words are graded by length.

The database contains all binary words of size at most 9.

A binary tree is uniquely represented as a dot (empty tree) or as a sorted list of binary trees.
 Binary trees are graded by the number of internal nodes.
 The database contains all binary trees of size at most 8.
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