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# Excess-3

Excess-3, 3-excess or 10-excess-3 binary code (often abbreviated as XS-3, 3XS or X3) or Stibitz code (after George Stibitz, who built a relay-based adding machine in 1937) is a self-complementary binary-coded decimal (BCD) code and numeral system. [1]

## Aiken code

The Aiken code (also known as 2421 code) is a complementary binary-coded decimal (BCD) code.

## Algorithm

In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.

## American Institute of Electrical Engineers

The American Institute of Electrical Engineers (AIEE) was a United States-based organization of electrical engineers that existed from 1884 through 1962.

## Binary number

In mathematics and digital electronics, a binary number is a number expressed in the base-2 numeral system or binary numeral system, which uses only two symbols: typically 0 (zero) and 1 (one).

## Binary-coded decimal

In computing and electronic systems, binary-coded decimal (BCD) is a class of binary encodings of decimal numbers where each decimal digit is represented by a fixed number of bits, usually four or eight.

## Bit

The bit (a portmanteau of binary digit) is a basic unit of information used in computing and digital communications.

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## Constant-weight code

In coding theory, a constant-weight code, also called an m-of-n code, is an error detection and correction code where all codewords share the same Hamming weight.

## David Van Nostrand

David Van Nostrand (December 5, 1811, New York City – June 14, 1886, New York City) was a New York City publisher.

## George Stibitz

George Robert Stibitz (April 30, 1904 – January 31, 1995) was a Bell Labs researcher internationally recognized as one of the fathers of the modern first digital computer.

## Gray code

The reflected binary code (RBC), also known just as reflected binary (RB) or Gray code after Frank Gray, is an ordering of the binary numeral system such that two successive values differ in only one bit (binary digit).

## Hamming code

In telecommunication, Hamming codes are a family of linear error-correcting codes.

## Hamming distance

In information theory, the Hamming distance between two strings of equal length is the number of positions at which the corresponding symbols are different.

## IBM

The International Business Machines Corporation (IBM) is an American multinational technology company headquartered in Armonk, New York, United States, with operations in over 170 countries.

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## Integer overflow

In computer programming, an integer overflow occurs when an arithmetic operation attempts to create a numeric value that is outside of the range that can be represented with a given number of bits – either larger than the maximum or lower than the minimum representable value.

## ITU-T

The ITU Telecommunication Standardization Sector (ITU-T) is one of the three sectors (divisions or units) of the International Telecommunication Union (ITU); it coordinates standards for telecommunications.

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## John Wiley & Sons

John Wiley & Sons, Inc., also referred to as Wiley, is a global publishing company that specializes in academic publishing.

## Method of complements

In mathematics and computing, the method of complements is a technique used to subtract one number from another using only addition of positive numbers.

## Numeral system

A numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner.

## Offset binary

Offset binary, also referred to as excess-K, excess-N, excess code or biased representation, is a digital coding scheme where all-zero corresponds to the minimal negative value and all-one to the maximal positive value.

## Ones' complement

The ones' complement of a binary number is defined as the value obtained by inverting all the bits in the binary representation of the number (swapping 0s for 1s and vice versa).

## Positional notation

Positional notation or place-value notation is a method of representing or encoding numbers.

## Signed number representations

In computing, signed number representations are required to encode negative numbers in binary number systems.

## Simon & Schuster

Simon & Schuster, Inc., a subsidiary of CBS Corporation, is an American publishing company founded in New York City in 1924 by Richard Simon and Max Schuster.

Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.

## Typographical error

A typographical error (often shortened to typo), also called misprint, is a mistake made in the typing process (such as a spelling mistake) of printed material.

## VHDL

VHDL (VHSIC Hardware Description Language) is a hardware description language used in electronic design automation to describe digital and mixed-signal systems such as field-programmable gate arrays and integrated circuits.

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## References

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