Talk:Excess-3

Example, please

Put in a negative example, as that's the whole point of biasing? 61.68.169.114 (talk) 14:06, 17 April 2008 (UTC)[reply]

Snapshot 2009

Excess-3 binary-coded decimal (XS-3), also called biased representation or Excess-N, is a numeral system used on some older computers that uses a pre-specified number N as a biasing value. It is a way to represent values with a balanced number of positive and negative numbers. 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):
The smallest binary number represents the smallest value. (i.e. 0 − Excess Value) The greatest binary number represents the largest value. (i.e. 2 N+1 − Excess Value − 1) Decimal Binary Decimal Binary Decimal Binary Decimal Binary −3 0000 1 0100 5 1000 9 1100 −2 0001 2 0101 6 1001 10 1101 −1 0010 3 0110 7 1010 11 1110 0 0011 4 0111 8 1011 12 1111
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 nines' complemented (for subtraction) as easily as a binary number can be ones' complemented; just invert all bits.
Adding Excess-3 works on a different algorithm than BCD coding or regular binary numbers. When you add two XS-3 numbers together, the result is not an XS-3 number. For instance, when you add 1 and 0 in XS-3 the answer seems to be 4 instead of 1. In order to correct this problem, when you are finished adding each digit, you have to subtract 3 (binary 11) if the digit is less than decimal 10 and substract six if the number is greater than or equal to decimal 10 (thus causing the number to wrap).

—Preceding unsigned comment added by 114.143.65.246 (talk) 13:01, 7 November 2009 (UTC)[reply]

Motivation section contradicts earlier chart

The motivation section says that one of the advantages of Excess-3 is that 0000 and 1111 are not used... but in the chart in the section directly above, those numbers are used... so which is it? This needs to be clarified. Also, the chart itself is a bit of a mess. Putting in "pseudo-tetrade" in the BCD column is nonsense. Why not just show the actual BCD representation for those numbers? MrAureliusR_Talk! 02:33, 15 April 2022 (UTC)[reply]

Google hits for "tetrade", in the sense it is used here, point to texts of German origin. 99.112.121.67 (talk) 08:07, 27 September 2022 (UTC)[reply]