Why are binary numbers usually longer than their decimal equivalents?

Binary numbers are typically longer than their decimal equivalents because a binary digit, or bit, carries less information than a decimal digit.1

In the decimal system, each digit can represent one of 10 possibilities (0 through 9), whereas a binary digit distinguishes between only two possibilities (0 or 1). Because each binary place value represents a power of 2 rather than a power of 10, more digits are required to represent the same numerical value.123

While this results in longer strings of characters, the binary number system is highly advantageous for computers. It is easier to engineer hardware to distinguish between two states—such as "on-off" or "open-closed"—than among 10 distinct states. Furthermore, these binary digits allow machines to simultaneously process numerical data and logic, as the binary values 1 and 0 effectively represent the dichotomies of true and false or yes and no.14