- Excess-3
**Excess-3**binary coded decimal (XS-3), also called**biased**representation or**Excess-N**, is anumeral 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 fourbit s 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. 2^{N}- 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' complement ed; 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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