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Question

# Convert $\text{F}111_{\text {sixteen }}$ to binary.

Solution

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Answered 2 years ago
Answered 2 years ago
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$\text{F}111_{sixteen} \to ???_{two}$

Because 16 and 2 are powers of 2, there is a shortcut to convert the numbers using Table 13 p.167. We divide the number in $hexadecimal$ in separate digits:

\begin{aligned} &\text{\:F}\hspace{4em}1\hspace{4em}1\hspace{4em}1\\ &\textcolor{#c34632}{\downarrow}\hspace{4em}\textcolor{#c34632}{\downarrow}\hspace{4em}\textcolor{#c34632}{\downarrow}\hspace{4em}\textcolor{#c34632}{\downarrow}\\ &1111\hspace{2em}0001\hspace{3em}0001\hspace{2em}0001 \end{aligned}

Hence, the number in binary form is:

$1111'0001'0001'0001_{two} = 1111000100010001_{two}$

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