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# Excess-3

Excess-3 binary coded decimal (XS-3), also called biased representation or Excess-N, is a numeral system used on some older computers that uses a pre-specified number "N" as a biasing value. It is a way to represent values with a balanced number of positive and negative numbers. In XS-3, numbers are represented as decimal digits, and each digit is represented by four bits as the BCD value plus 3 (the "excess" amount):

* The smallest binary number represents the smallest value. (i.e. 0 - Excess Value)
* The greatest binary number represents the largest value. (i.e. 2N - Excess Value - 1)

To encode a number such as 127, then, one simply encodes each of the decimal digits as above, giving (0100, 0101, 1010).

The primary advantage of XS-3 coding over BCD coding is that a decimal number can be nines' complemented (for subtraction) as easily as a binary number can be ones' complemented; just invert all bits.

Adding Excess-3 works on a different algorithm than BCD coding or regular binary numbers. When you add two XS-3 numbers together, the result is not an XS-3 number. For instance, when you add 1 and 0 in XS-3 the answer seems to be 4 instead of 1. In order to correct this problem, when you are finished adding each digit, you have to subtract 3 (binary 11) if the digit is less than decimal 10 and add three if the number is greater than or equal to decimal 10.

ee also

*Gray code

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### Look at other dictionaries:

• Excess — Ex*cess , n. [OE. exces, excess, ecstasy, L. excessus a going out, loss of self possession, fr. excedere, excessum, to go out, go beyond: cf. F. exc[ e]s. See {Exceed}.] 1. The state of surpassing or going beyond limits; the being of a measure… …   The Collaborative International Dictionary of English

• excess — ex·cess adj: more than a usual or specified amount; specif: additional to an amount specified under another insurance policy excess coverage excess insurance Merriam Webster’s Dictionary of Law. Merriam Webster. 1996 …   Law dictionary

• excess — n Excess, superfluity, surplus, surplusage, overplus denote something which goes beyond a limit or bound. Excess applies to whatever exceeds a limit, measure, bound, or accustomed degree {in measure rein thy joy; scant this excess Shak.} {the… …   New Dictionary of Synonyms

• excess — [ek ses′, ikses′; ] also, esp.for adj. [, ek′ses΄] n. [ME & OFr exces < L excessus < pp. of excedere: see EXCEED] 1. action or conduct that goes beyond the usual, reasonable, or lawful limit 2. lack of moderation; intemperance;… …   English World dictionary

• Excess — is a state of something being present beyond a requisite amount. In certain contexts, it has a more specialized meaning:* In insurance, similar to deductible. * In chemistry, describing any reagent that is not the limiting reagent. * Excess is… …   Wikipedia

• excess — (n.) late 14c., from O.Fr. exces (14c.) excess, extravagance, outrage, from L. excessus departure, a going beyond the bounds of reason or beyond the subject, from stem of excedere to depart, go beyond (see EXCEED (Cf. exceed)). As an adjective… …   Etymology dictionary

• excess — [n1] overabundance of something balance, by product, enough, exorbitance, exuberance, fat, fulsomeness, glut, inundation, lavishness, leavings, leftover, luxuriance, nimiety, overdose, overflow, overkill, overload, overmuch, overrun, oversupply,… …   New thesaurus

• excess — ► NOUN 1) an amount that is more than necessary, permitted, or desirable. 2) lack of moderation, especially in eating or drinking. 3) (excesses) outrageous or immoderate behaviour. 4) Brit. a part of an insurance claim to be paid by the insured.… …   English terms dictionary

• excess — in an insurance policy, excess clauses specify that the policyholder will be responsible for a portion of claims under certain conditions. Glossary of Business Terms The dollar amount by which the equity exceeds the margin requirements in a… …   Financial and business terms

• excess — ♦♦♦ excesses (The noun is pronounced [[t]ɪkse̱s[/t]]. The adjective is pronounced [[t]e̱kses[/t]].) 1) N VAR: with supp, usu a N of n An excess of something is a larger amount than is needed, allowed, or usual. An excess of houseplants in a small …   English dictionary