It is also more difficult to write the zero pattern to magnetic media. A fault in a memory or basic transmission line may result in these codes. Because a 4-bit integer can only hold values 0 to 15, an excess of 6 means that any sum over 9 will overflow (produce a carry out).Īnother advantage is that the codes 00 are not used for any digit. This works because, after adding two digits, an "excess" value of 6 results in the sum. Also, when the sum of two excess-3 digits is greater than 9, the carry bit of a 4-bit adder will be set high. The primary advantage of excess-3 coding over non-biased coding is that a decimal number can be nines' complemented (for subtraction) as easily as a binary number can be ones' complemented: just by inverting all bits.
(In 4-bit binary, subtracting binary 1101 is equivalent to adding 0011 and vice versa.) In order to correct this problem, after adding two digits, it is necessary to remove the extra bias by subtracting binary 0011 (decimal 3 in unbiased binary) if the resulting digit is less than decimal 10, or subtracting binary 1101 (decimal 13 in unbiased binary) if an overflow (carry) has occurred. For instance, after adding 1 (0100 in excess-3) and 2 (0101 in excess-3), the sum looks like 6 (1001 in excess-3) instead of 3 (0110 in excess-3). After adding two excess-3 digits, the raw sum is excess-6. To encode a number such as 127, one simply encodes each of the decimal digits as above, giving (0100, 0101, 1010).Įxcess-3 arithmetic uses different algorithms than normal non-biased BCD or binary positional system numbers.
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In excess-3 code, numbers are represented as decimal digits, and each digit is represented by four bits as the digit value plus 3 (the "excess" amount): Biased codes (and Gray codes) are non-weighted codes.
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Excess-3 code was used on some older computers as well as in cash registers and hand-held portable electronic calculators of the 1970s, among other uses.īiased codes are a way to represent values with a balanced number of positive and negative numbers using a pre-specified number N as a biasing value. Excess-3, 3-excess or 10-excess-3 binary code (often abbreviated as XS-3, 3XS or X3 ), shifted binary 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.
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