13. (15 points) Binary is a number system widely adopted in computer technology, and the method of converting binary numbers to decimal numbers is as follows:
$$
\begin{array}{l}
(101)_{2}=1 \times 2^{2}+0 \times 2^{1}+1 \times 2^{0}=(5)_{10} ; \quad \quad \text { (Note: } 2^{n}=\underbrace{2 \times 2 \times \ldots . . \times 2}_{n \uparrow 2}, 2^{0}=1) \\
(11011)_{2}=1 \times 2^{4}+1 \times 2^{3}+0 \times 2^{2}+1 \times 2^{1}+1 \times 2^{0}=(27)_{10} ; \\
(1100111)_{2}=1 \times 2^{6}+1 \times 2^{5}+0 \times 2^{4}+0 \times 2^{3}+1 \times 2^{2}+1 \times 2^{1}+1 \times 2^{0}=(119)_{10} ; \\
(111101111)_{2}=1 \times 2^{8}+1 \times 2^{7}+1 \times 2^{6}+1 \times 2^{5}+0 \times 2^{4}+1 \times 2^{3}+1 \times 2^{2}+1 \times 2^{1}+1 \times 2^{0}=(495)_{10} ;
\end{array}
$$

Then, converting the binary number 11111011111 to a decimal number, what is the result?
13. (15 points) Binary is a number system widely adopted in computer technology, and the method of converting binary numbers to decimal numbers is as follows:
$$
\begin{array}{l}
(101) 2=1 \times 2^{2}+0 \times 2^{1}+1 \times 2^{0}=(5)_{10} \text {; } \\
\text { (Note: } 2^{n}=\underbrace{2 \times 2 \times \ldots . \times 2}_{n \uparrow 2}, 2^{0}=1 \text { ) } \\
\text { (11011) } 2=1 \times 2^{4}+1 \times 2^{3}+0 \times 2^{2}+1 \times 2^{1}+1 \times 2^{0}=(27)_{10} \text {; } \\
(1100111) 2=1 \times 2^{6}+1 \times 2^{5}+0 \times 2^{4}+0 \times 2^{3}+1 \times 2^{2}+1 \times 2^{1}+1 \times 2^{0}=(119)_{10} \text {; } \\
(111101111)_{2}=1 \times 2^{8}+1 \times 2^{7}+1 \times 2^{6}+1 \times 2^{5}+0 \times 2^{4}+1 \times 2^{3}+1 \times 2^{2}+1 \times 2^{1}+1 \times 2^{0}=(495)_{10} \text {; } \\
\end{array}
$$

Then, converting the binary number 11111011111 to a decimal number, what is the result?
【Solution】Solution: (11111011111) 2
$$
\begin{array}{l}
=1 \times 2^{10}+1 \times 2^{9}+1 \times 2^{8}+1 \times 2^{7}+1 \times 2^{6}+0 \times 2^{5}+1 \times 2^{4}+1 \times 2^{3}+1 \times 2^{2}+1 \times 2^{1}+1 \times 2^{0} \\
=1024+512+256+128+64+0+16+8+4+2+1 \\
=(2015)_{10}
\end{array}
$$

Answer: It is 2015.