# Definitions for excess-3ex·cess-3

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1. Excess-3

Excess-3 binary or Stibitz code, also called biased representation or Excess-N, is a complementary BCD code and numeral system. Excess-3 was used on some older computers as well as in cash registers and hand held portable electronic calculators of the 1970's, among other uses. It is a way to represent values with a balanced number of positive and negative numbers using a pre-specified number N as a biasing value. It is a nonweighted code. In XS-3, numbers are represented as decimal digits, and each digit is represented by four bits as the digit value plus 3: ⁕The smallest binary number represents the smallest value. ⁕The greatest binary number represents the largest value. To encode a number such as 127, then, one simply encodes each of the decimal digits as above, giving. The primary advantage of XS-3 coding over non-biased coding is that a decimal number can be nines' complemented as easily as a binary number can be ones' complemented; just invert all bits. In addition, when the sum of two XS-3 digits is greater than 9, the carry bit of a four bit adder will be set high. This works because, when adding two numbers that are greater or equal to zero, an "excess" value of six results in the sum. Since a four bit integer can only hold values 0 to 15, an excess of six means that any sum over nine will overflow.

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### Numerology

1. Chaldean Numerology

The numerical value of excess-3 in Chaldean Numerology is: 6

2. Pythagorean Numerology

The numerical value of excess-3 in Pythagorean Numerology is: 3

## Translations for excess-3

• الزائد-3

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