BalancedNumerals

Balanced base $b$ (odd): digits run $-(b-1)/2,\dots,(b-1)/2$ — it spells negative integers with no sign at all, and rounding to nearest is just truncation. Balanced ternary ($b=3$) is the famous case.

BalancedNumerals(b)the system, digits $-(b-1)/2,\dots,(b-1)/2$

Typed signatures

Type	Package	Applies
(integer) -> value	numerals	always

Domain: Numeral systems

Examples

Basic #

No sign needed: $-5 = -9 + 3 + 1$

live ↗

In$\mathrm{IntegerDigits}(-5, \mathrm{BalancedNumerals}(3))$Out$\bigl\lbrack-1, 1, 1\bigr\rbrack$

$100 = 81 + 27 - 9 + 1$

live ↗

In$\mathrm{IntegerDigits}(100, \mathrm{BalancedNumerals}(3))$Out$\bigl\lbrack1, 1, -1, 0, 1\bigr\rbrack$

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Examples	2

See also: IntegerDigits, NegativeNumerals, BalancedRadix