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Genaueres zur Gleitpunktdarstellung nach IEEE-Standard siehe Extraseite.
Maschinengenauigkeit von Exceldownload *.xls
Prof. Dr. Dörte Haftendorn Okt 02 Mit 25 Stellen ausgeschrieben
Die Maschinengenauigkeit ist die kleinste Zahl, deren Addition zu 1 von der Maschine noch gemerkt wird.
i 1+10^ (-i) das -1 j 1+2^ (-j) das -1 1+2^ (-j) das -1 j
1 1,1 0,1 1 1,5 0,5 1,5000000000000000000000000 0,5000000000000000000000000 1
2 1,01 0,01 2 1,25 0,25 1,2500000000000000000000000 0,2500000000000000000000000 2
3 1,001 0,001 3 1,125 0,125 1,1250000000000000000000000 0,1250000000000000000000000 3
4 1,0001 1E-04 4 1,0625 0,0625 1,0625000000000000000000000 0,0625000000000000000000000 4
5 1,00001 1E-05 5 1,03125 0,03125 1,0312500000000000000000000 0,0312500000000000000000000 5
6 1,000001 1E-06 6 1,015625 0,015625 1,0156250000000000000000000 0,0156250000000000000000000 6
7 1,0000001 1E-07 7 1,0078125 0,0078125 1,0078125000000000000000000 0,0078125000000000000000000 7
8 1,00000001 1E-08 8 1,00390625 0,00390625 1,0039062500000000000000000 0,0039062500000000000000000 8
9 1,000000001 1E-09 9 1,00195313 0,001953125 1,0019531250000000000000000 0,0019531250000000000000000 9
10 1 1E-10 10 1,00097656 0,000976563 1,0009765625000000000000000 0,0009765625000000000000000 10
11 1 1E-11 11 1,00048828 0,000488281 1,0004882812500000000000000 0,0004882812500000000000000 11
12 1 1,0001E-12 12 1,00024414 0,000244141 1,0002441406250000000000000 0,0002441406250000000000000 12
13 1 9,992E-14 13 1,00012207 0,00012207 1,0001220703125000000000000 0,0001220703125000000000000 13
14 1 9,992E-15 14 1,00006104 6,10352E-05 1,0000610351562500000000000 0,0000610351562500000000000 14
15 1 0 15 1,00003052 3,05176E-05 1,0000305175781200000000000 0,0000305175781250000000000 15
      16 1,00001526 1,52588E-05 1,0000152587890600000000000 0,0000152587890625000000000 16
      17 1,00000763 7,62939E-06 1,0000076293945300000000000 0,0000076293945312500000000 17
      18 1,00000381 3,8147E-06 1,0000038146972600000000000 0,0000038146972656250000000 18
      19 1,00000191 1,90735E-06 1,0000019073486300000000000 0,0000019073486328125000000 19
      20 1,00000095 9,53674E-07 1,0000009536743100000000000 0,0000009536743164062500000 20
      21 1,00000048 4,76837E-07 1,0000004768371500000000000 0,0000004768371582031250000 21
      22 1,00000024 2,38419E-07 1,0000002384185700000000000 0,0000002384185791015620000 22
      23 1,00000012 1,19209E-07 1,0000001192092800000000000 0,0000001192092895507810000 23
      24 1,00000006 5,96046E-08 1,0000000596046400000000000 0,0000000596046447753906000 24
      25 1,00000003 2,98023E-08 1,0000000298023200000000000 0,0000000298023223876953000 25
      26 1,00000001 1,49012E-08 1,0000000149011600000000000 0,0000000149011611938477000 26
      27 1,00000001 7,45058E-09 1,0000000074505800000000000 0,0000000074505805969238300 27
      28 1 3,72529E-09 1,0000000037252900000000000 0,0000000037252902984619100 28
      29 1 1,86265E-09 1,0000000018626400000000000 0,0000000018626451492309600 29
      30 1 9,31323E-10 1,0000000009313200000000000 0,0000000009313225746154790 30
      31 1 4,65661E-10 1,0000000004656600000000000 0,0000000004656612873077390 31
      32 1 2,32831E-10 1,0000000002328300000000000 0,0000000002328306436538700 32
      33 1 1,16415E-10 1,0000000001164200000000000 0,0000000001164153218269350 33
      34 1 5,82077E-11 1,0000000000582100000000000 0,0000000000582076609134674 34
      35 1 2,91038E-11 1,0000000000291000000000000 0,0000000000291038304567337 35
Also ist die Maschinengenauigkeit von Excel 36 1 1,45519E-11 1,0000000000145500000000000 0,0000000000145519152283669 36
37 1 7,27596E-12 1,0000000000072800000000000 0,0000000000072759576141834 37
38 1 3,63798E-12 1,0000000000036400000000000 0,0000000000036379788070917 38
39 1 1,81899E-12 1,0000000000018200000000000 0,0000000000018189894035459 39
40 1 9,09495E-13 1,0000000000009100000000000 0,0000000000009094947017729 40
2^(-49) 41 1 4,54747E-13 1,0000000000004500000000000 0,0000000000004547473508865 41
42 1 2,27374E-13 1,0000000000002300000000000 0,0000000000002273736754432 42
43 1 1,13687E-13 1,0000000000001100000000000 0,0000000000001136868377216 43
=1,77636*10^(-15) 44 1 5,68434E-14 1,0000000000000600000000000 0,0000000000000568434188608 44
45 1 2,84217E-14 1,0000000000000300000000000 0,0000000000000284217094304 45
46 1 1,42109E-14 1,0000000000000100000000000 0,0000000000000142108547152 46
      47 1 7,10543E-15 1,0000000000000100000000000 0,0000000000000071054273576 47
Mantissenlänge: dual 49+3 Stellen , also insgesamt 52 Bit 48 1 3,55271E-15 1,0000000000000000000000000 0,0000000000000035527136788 48
49 1 1,77636E-15 1,0000000000000000000000000 0,0000000000000017763568394 49
50 1 0 1,0000000000000000000000000 0,0000000000000000000000000 50
51 1 0 1,0000000000000000000000000 0,0000000000000000000000000 51
52 1 0 1,0000000000000000000000000 0,0000000000000000000000000 52
      53 1 0 1,0000000000000000000000000 0,0000000000000000000000000 53
siehe auch Bereich-Seite 54 1 0 1,0000000000000000000000000 0,0000000000000000000000000 54

Letzte Aktualisierung 05.10.2002
Durch Prof. Dr. Dörte Haftendorn Genaueres zur Gleitpunktdarstellung nach IEEE-Standard siehe Extraseite.

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Inhalt und Webbetreuung Prof. Dr. Dörte Haftendorn April 2002, update 06. November 2011