Excess-3

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Excess-3 binary coded decimal (XS-3) is a numeral system used in some old computers. 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):

Digit Bits      Digit Bits

  0   0011        5   1000

  1   0100        6   1001

  2   0101        7   1010

  3   0110        8   1011

  4   0111        9   1100

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 nine's complemented (for subtraction) as easily as a binary number can be one's complemented, just invert all bits.