Binary Notation/Examples/47
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Example of Binary Notation
The number written in decimal notation as $47$ is expressed in binary notation as $101111_2$.
Proof
| \(\ds 47\) | \(=\) | \(\ds 1 \times 2^5 + 0 \times 2^4 + 1 \times 2^3 + 1 \times 2^2 + 1 \times 2^1 + 1 \times 2^0\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 32 + 0 + 8 + 4 + 2 + 1\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 101111_2\) |
$\blacksquare$
Sources
- 1971: George E. Andrews: Number Theory ... (previous) ... (next): $\text {1-2}$ The Basis Representation Theorem: Exercise $2$