Binary string
\(0100010001101001011100110110001101110010011001010111010001101111011100000110100101100001\)
A binary string is a string whose alphabet is \(\set{0, 1}.\) Characters in a binary string are called bits. Binary strings of length \(n\) are often called \(n\)-bit binary strings.
The set of all binary strings of length \(k\) is denoted \(B^k.\) Additionally, the set of all binary strings of any length is denoted \(B^*\), defined as the infinite union of all sets \(B^k\) such that \(k \geq 0\): \(B^* = B^0 \cup B^1 \cup B^2 \cup ...\)
Of course, \(B^0 = \set{\lambda}\), because the only string of length \(0\) is the empty string.