By Arndt J.
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Additional info for Matters computational (algorithms for programmers)
Example text
Be warned that the parity flag of many CPUs is the complement of the above. With the x86-architecture the parity bit also only takes into account the lowest byte. 3 Incrementing (counting) in Gray code k: 0: 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15: 16: 17: g(k) ....... 1. 11. 1.. 11.. 111. 1. 1... 11... 1 g(2*k) ....... 11. 11.. 1. 11... 1111. 1.. 1. 11.... 11 g(k) ...... 1. 11. 1.. 11.. 111. 1. 1... 11... 1 p . 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 diff ...... +1. +1.. 1-1. +1... + p . 1 .
11... 1111. 1.. 1. 11.... 11 g(k) ...... 1. 11. 1.. 11.. 111. 1. 1... 11... 1 p . 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 diff ...... +1. +1.. 1-1. +1... + p . 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 . 16-B: The Gray code equals the Gray code of doubled value shifted to the right once. Equivalently, we can separate the lowest bit which equals the parity of the other bits. The last column shows that the changes with each increment always happen one position left of the rightmost bit. Let g(k) be the Gray code of a number k.
A1=11111111 a1=11111111 a1=........ a1=........ a1=11111111 a1=11111111 a1=........ a1=........ a1=11111111 a1=11111111 a1=........ a1=........ a2=........ a2=........ a2=........ a2=11111111 a2=11111111 a2=11111111 a2=11111111 a2=........ a2=........ a2=........ a2=........ a2=11111111 a2=11111111 a2=11111111 a2=11111111 a2=........ a2=........ a3=........ a3=........ a3=........ a3=........ a3=........ a3=........ a3=........ a3=11111111 a3=11111111 a3=11111111 a3=11111111 a3=11111111 a3=11111111 a3=11111111 a3=11111111 a3=........