Rechnerorganisation: Hardware und Software digitaler Rechner by Dr.-ing. Hans Liebig (auth.)

By Dr.-ing. Hans Liebig (auth.)

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R;;' 0) then qn == 1 else qn == 0; for i from n - 1 ~ -1 to a do r----------------, IR:=R·2-(2·q. D·1 1+1' I I !! (R ;;. 0) then qi 1 II IL ________________ else qi a I == == ~ I I I ___________________ R := R - (qo - 1) • D L Multiplikation r------------------~ D :== D • 2n; R :== 0; qn == 1 - qn-1; R := R + (~ - 1) • D; for i from 0 ~ 1 to n - 1 do r---------------, II R :== (R + (2q. 1- 1) . D)/2 I L _______________ 1+ I ~ ~-----------------~ Fur ungerade Zahlen Q bei a und fur gerade Zahlen bei -D beginnend, wird R durch Additionen und Subtraktionen Schritt fUr Schritt aufgebaut.

12 und fUr Rn = +8· D + RO. Es entsteht U= 01000 = +8 und Ro < 0 I Bild 1. 14 Division ohne Riickstellen des Rests bei ungerad- und geradzahligen Quotienten 1m Fall Rn = 9· D + RO entsteht Q = 01001 = +9 mit positivem Rest, im Falle Rn = 8· D + RO entsteht Q = 01000 = +8 mit negativem Rest. Es ist fUr dieses Verfahren charakteristisch, daB aHe geraden Zahlen Q falschlicherweise einen negativen Rest haben, der durch eine nachfolgende Addition von D korrigiert werden muB. Dadurch entsteht in jedem Fall ein positiver Rest, der gegebenenfalls erneut korrigiert werden muB (vgl.

Gegeben ist eine ganze Dualzahl X = x n _ 1 x n _ 2 ••• ~ in 2-Komplement-Darstellung. Die Algorith- men berechnen die einzelnen Ergebnisziffern Y = Y 1 Y 2 ••• yO. Sie benutzen nndazu die HilfsgroBen (Ubertrage) u O' u 1 , ••• , un _ 1 und zeigen eine Bereichsiiberschreitung (Uberlauf) durch ii an. 1 Vorwarlszahlen Y = X + 1 r------------------, uo = 1, for i from 0 ~ 1 to n - 1 do r--------, I u. , 1 1 I 1+ I I y. = x. EF> u. 1 1 1 I I I I I I '--------_.... 2 Riickwartszahlen Y = X - 1 r------------------, o = 1, U for i from 0 ~ 1 to n - 1 do r--------, I u.

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