examples of uniqueness of digital representation of small numbers in a few bases

While a string of digits is not unique to any base $b$, within each base $b$ the base $b$ representation of an integer $n$ is unique. The following table gives the base 2 (binary) through base 10 (decimal) representations of $n$ from 1 to 50. It will be seen how “10” occurs in several cells diagonally in the table, but in each column it corresponds to the case $n=b$ only. Likewise, “11” also occurs diagonally, but in each column it corresponds to $n=b+1$ only. One other generality to mention: the representation $n$ is the same for all bases $b>n$.