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)
“The importance of its hat to a form becomes
More definite. The sweeping brim of the hat
Makes of the form Most Merciful Capitan,
If the observer says so....”
—Wallace Stevens (1879–1955)