1957 AHSME Problem 19

The base of the decimal number system is ten, meaning, for example, that 123 = 1\cdot 10^2 + 2\cdot 10 + 3. In the binary system, which has base two, the first five positive integers are 1,\,10,\,11,\,100,\,101. The numeral 10011 in the binary system would then be written in the decimal system as:

\textbf{(A)}\ 19 \qquad \textbf{(B)}\ 40\qquad \textbf{(C)}\ 10011\qquad \textbf{(D)}\ 11\qquad \textbf{(E)}\ 7

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.