Basis Expansion/Examples/3 Quarters in Binary
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Example of Basis Expansion
The fraction $\dfrac 3 4$ has a basis expansion in binary (base $2$) notation as:
- $\sqbrk {0 \cdotp 11}_2$
Proof
| \(\ds \dfrac 3 4\) | \(=\) | \(\ds \dfrac 1 2 + \dfrac 1 4\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 1 \times 2^{-1} + 1 \times 2^{-2}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \sqbrk {0 \cdotp 11}_2\) |
$\blacksquare$
Sources
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): expansion: 2.