Discussion
What is the binary equivalent of the decimal number \((25)_{10}\) ?
Answer: C
The binary form is \((11001)_{2}\).
Write 25 as a sum of powers of two, or divide by 2 repeatedly and read the remainders upward.
\[ \begin{aligned} 25 &= 16 + 8 + 1 \\ &= 2^{4} + 2^{3} + 2^{0} \\ &= (11001)_{2} \end{aligned} \]
Check the others: \((11011)_{2} = 27\), \((10011)_{2} = 19\) and \((10001)_{2} = 17\). Only 11001 gives 25.
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