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Q. The decimal equivalent of the binary number $(11010.101)_2$ is

WBJEEWBJEE 2010Semiconductor Electronics: Materials Devices and Simple Circuits

Solution:

The decimal equivalent can be found as follows,
$(11010.101)_{2}=0 \times 2^{0}+1 \times 2^{1}+0 \times 2^{2}$
$\quad+1 \times 2^{3}+1 \times 2^{4}+1 \times 2^{-1}+0 \times 2^{-2}+1 \times 2^{-3}$
$=0+2+0+8+16+\frac{1}{2}+0+\frac{1}{8}$
$=26+\frac{5}{8}=\frac{213}{8} \approx 26.625$