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:
“Virtues are not emotions. Emotions are movements of appetite, virtues dispositions of appetite towards movement. Moreover emotions can be good or bad, reasonable or unreasonable; whereas virtues dispose us only to good. Emotions arise in the appetite and are brought into conformity with reason; virtues are effects of reason achieving themselves in reasonable movements of the appetites. Balanced emotions are virtue’s effect, not its substance.”
—Thomas Aquinas (c. 1225–1274)
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—Henry David Thoreau (1817–1862)