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:
“With a balanced combination of the two principal energies from mother and father, a girl can both be in touch with her womanly strengths and be a powerful force in the world—strong and nurturing, decisive and caring, goal- oriented and aware of the needs of others. She has the courage to voice what she thinks and feels and the strength to follow her destiny.”
—Jeanne Elium (20th century)
“The Republican form of government is the highest form of government; but because of this it requires the highest type of human nature—a type nowhere at present existing.”
—Herbert Spencer (1820–1903)