Basis Expansion/Examples/5 in Binary
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Example of Basis Expansion
The number $5$ has a basis expansion in binary (base $2$) notation as:
- $\sqbrk {101}_2$
Proof
| \(\ds \sqbrk {101}_2\) | \(=\) | \(\ds 1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 4 + 0 + 1\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 5\) |
$\blacksquare$
Sources
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): expansion: 2.