Balanced Form
In balanced form, the digits are drawn from a range to, where typically . For balanced forms, odd base numbers are advantageous. With an odd base number, truncation and rounding become the same operation, and all the digits except 0 are used in both positive and negative form.
A notable example is balanced ternary, where the base is, and the numerals have the values −1, 0 and +1 (rather than 0, 1, and 2 as in the standard ternary numeral system). Balanced ternary uses the minimum number of digits in a balanced form. Balanced decimal uses digits from −5 to +4. Balanced base nine, with digits from −4 to +4 provides the advantages of an odd-base balanced form with a similar number of digits, and is easy to convert to and from balanced ternary.
Other notable examples include Booth encoding and non-adjacent form, both of which use a base of, and both of which use numerals with the values −1, 0, and +1 (rather than 0 and 1 as in the standard binary numeral system).
Read more about this topic: Signed-digit Representation
Famous quotes containing the words balanced and/or form:
“I balanced all, brought all to mind,
The years to come seemed waste of breath,
A waste of breath the years behind
In balance with this life, this death.”
—William Butler Yeats (1865–1939)
“It may be said that the elegant Swann’s simplicity was but another, more refined form of vanity and that, like other Israelites, my parents’ old friend could present, one by one, the succession of states through which had passed his race, from the most naive snobbishness to the worst coarseness to the finest politeness.”
—Marcel Proust (1871–1922)