The base of the decimal number system is ten, meaning, for example, that $ 123 \equal{} 1\cdot 10^2 \plus{} 2\cdot 10 \plus{} 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$
To convert the binary number \(10011_2\) to its decimal equivalent, we need to express it as a sum of powers of 2. Each digit in the binary number represents a power of 2, starting from \(2^0\) on the right.

1. Write down the binary number and its corresponding powers of 2:
   \[
   10011_2 = 1 \cdot 2^4 + 0 \cdot 2^3 + 0 \cdot 2^2 + 1 \cdot 2^1 + 1 \cdot 2^0
   \]

2. Calculate each term:
   \[
   1 \cdot 2^4 = 1 \cdot 16 = 16
   \]
   \[
   0 \cdot 2^3 = 0 \cdot 8 = 0
   \]
   \[
   0 \cdot 2^2 = 0 \cdot 4 = 0
   \]
   \[
   1 \cdot 2^1 = 1 \cdot 2 = 2
   \]
   \[
   1 \cdot 2^0 = 1 \cdot 1 = 1
   \]

3. Sum all the terms:
   \[
   16 + 0 + 0 + 2 + 1 = 19
   \]

Therefore, the decimal equivalent of the binary number \(10011_2\) is \(19\).

The final answer is \(\boxed{19}\).