Binary Notation/Examples/23
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Example of Binary Notation
The number written in decimal notation as $23$ is expressed in binary notation as $10111_2$.
Proof
| \(\ds 23\) | \(=\) | \(\ds 1 \times 2^4 + 0 \times 2^3 + 1 \times 2^2 + 1 \times 2^1 + 1 \times 2^0\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 16 + 0 + 4 + 2 + 1\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 10111_2\) |
$\blacksquare$
Sources
- 1971: George E. Andrews: Number Theory ... (previous) ... (next): $\text {1-2}$ The Basis Representation Theorem: Example $\text {1-2}$