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The maximum three digit integer in the decimal system will be represented in the binary system by which one of the following?
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2230 Upvotes
Verified Answer
The correct answer is:
1111100111
The maximum three digit integer in decimal system $=999$. We go on dividing till we get a dividend $ < 2$ and write remainders from last to firstas shown below:
\begin{array}{l|l|l}
\hline 2 & 999 & \\
\hline 2 & 499 & 1 \\
\hline 2 & 249 & 1 \\
\hline 2 & 124 & 1 \\
\hline 2 & 62 & 0 \\
\hline 2 & 31 & 0 \\
\hline 2 & 15 & 1 \\
\hline 2 & 7 & 1 \\
\hline 2 & 3 & 1 \\
\hline & 1 & 1 \\
\hline
\end{array}
Hence, $(999)_{10}=(1111100111)_{2}$
\begin{array}{l|l|l}
\hline 2 & 999 & \\
\hline 2 & 499 & 1 \\
\hline 2 & 249 & 1 \\
\hline 2 & 124 & 1 \\
\hline 2 & 62 & 0 \\
\hline 2 & 31 & 0 \\
\hline 2 & 15 & 1 \\
\hline 2 & 7 & 1 \\
\hline 2 & 3 & 1 \\
\hline & 1 & 1 \\
\hline
\end{array}
Hence, $(999)_{10}=(1111100111)_{2}$
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