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Excess-3 Code (Stibitz)

Tool for decoding/encoding numbers via the Stibitz code also called Excess-3, a binary digital system similar to the BCD code, used by old processors coding each digit on 4 bits.

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Excess-3 Code (Stibitz) -

Tag(s) : Character Encoding

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Excess-3 Code (Stibitz)

Excess-3 Encoder/Converter

How to encrypt using Excess3 code?

The code Excess-3 (also called Stibitz code and sometimes shortcut XS3 or XS-3) is a 4-bit binary decimal code (like the BCD) created to optimize some calculations in base 10 on older processors.

The representation of a number in Excess-3 code is said to be biased because it has an offset of 3 (hence the 3 of XS-3) with the expected values and used by the conventional BCD code.

Example: 0 is coded 0011 in XS-3 whereas 0011 is 3 in BCD code.

The use of this offset allows a quick calculation trick for the complement to 9 (decimal) by inverting the bits, which is a big time saver for the calculation of subtractions by the processors.

Example: The digit 0 is coded 0011 in XS3 and its binary complement (inverting the 1's and 0's) is 1100 which corresponds to 9 in XS3.

The Decimal to Excess-3 conversion table:

DigitCode XS-3
00011
10100
20101
30110
40111
51000
61001
71010
81011
91100

Example: 123 is coded 0100,0101,0110

The codes 0000 or 1111 are not used to represent numbers, which can be interesting in the sending of communication (the sequences of 0 and 1 are often representative of reading errors)

How to convert a number coded in Excess3?

Split the binary number into groups of 4 bits and replace each group with the corresponding number in the conversion table (above).

Example: 11001011 is split 1100,1011 and corresponds respectively to the numbers 9,8, so the conversion into decimal is 98

How to recognize a Excess3 coded number?

The code has a binary representation, it is not really distinguishable from another binary code (BCD, Gray, etc.) apart from its particularity to avoid sequences of more than 7 0000000 or 1111111.

Any reference to the old processors, calculators or electronic cash machine of the 70s is a clue.

When Excess-3 have been invented ?

George Stibitz created a calculating machine based on this principle in 1937.

Source code

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