IIm18-Kreativaufgabe7
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Random Access Maschine - Paul Bachmann, Johannes Thies
RAM zur Ermittlung von \left\lfloor \sqrt{n} \right\rfloor
Geben Sie mind. ein RAM-Programm zur Berechnung der Funktion w : \N \mapsto \N mit w(n) = \left\lfloor \sqrt{n} \right\rfloor an.
Ermittlung der Potenz
| Befehlszähler | Anweisung | Bemerkung |
|---|---|---|
| | 0 | R0 = n | belegen von R0 mit einer natürlichen Zahl n |
| | 1 | R1 = 1 | fixer Wert für Inkrementierung/Dekrementierung |
| | 2 | R2 = R0 | Festlegung einer Zählvariable der Größe n |
| | 3 | R3 = 0 | R3 als Platzhalter für das Ergebnis |
| | 4 | R3 += R0 | Inkrementierung von R3 um n |
| | 5 | R2 -= R1 | Dekrementierung der Zählvariable |
| | 6 | IFZERO R2 GOTO 8 | wenn Zählvariable 0 ist, dann steht das Ergebnis in R3 |
| | 7 | GOTO 4 | R1 von R0 subtrahieren |
| | 8 | R0 = R3 | Ergebnis in R0 speichern |
| | 9 | STOP |
Realisierung des logischen Operators \leq
Kein RAM, sondern nur eine Visualisierung des Gedankenganges beim Vergleich zweier natürlicher Zahlen!
| Befehlszähler | Anweisung | Bemerkung |
|---|---|---|
| | 0 | R0 = a | belegen von R0 mit der ersten natürlichen Zahl a |
| | 1 | R1 = b | belegen von R1 mit der ersten natürlichen Zahl b |
| | 2 | R0 -= R1 | Dekrementierung von R0 um R1 |
| | 3 | IFZERO R0 GOTO ... | Wenn R0 = 0, dann ist der Ursprüngliche Wert von R0 \leq R1, wenn nicht, dann ist R0 > R1 |
Kombination beider Funktionen zur Ermittlung von \left\lfloor \sqrt{n} \right\rfloor
| Befehlszähler | Anweisung | Bemerkung |
|---|---|---|
| | 0 | R0 = n | belegen von R0 mit einer natürlichen Zahl n |
| | 1 | R1 = 1 | fixer Wert für Inkrementierung/Dekrementierung |
| | 2 | R2 += R1 | Zähler (Testvariable) |
| | 3 | R22 = R2 | Potenz Zählvariable |
| | 4 | R33 += R2 | Inkrementierung von R3 um R2 zur Berechnung der Potenz von Testvariable |
| | 5 | R22 -= R1 | Dekrementierung der Potenz Zählvariable |
| | 6 | IFZERO R22 GOTO 8 | wenn Zählvariable 0 ist, dann steht das Ergebnis in R33 |
| | 7 | GOTO 4 | Inkrementiere R33 solange bis Potenz Zählvariable 0 beträgt |
| | 8 | R33 -= R0 | kleinergelich Vergleich von Potenzergebnis und n |
| | 9 | IFZERO R33 GOTO 2 | wenn R33 0 beträgt, dann ist Potenz von Testvariable \leq n |
| | 10 | R2 -= R1 | Dekrementierung von R2 um 1, wenn Potenz der Testvariable zum ersten mal größer ist als n, da wir floor berechnen wollen |
| | 11 | R0 = R2 | Ergebnis in R0 speichern |
Beispiel für n = 10
| Anweisung | R0 | R1 | R1 | R22 | R33 |
|---|---|---|---|---|---|
| |R0 = n | 10 | 0 | 0 | 0 | 0 |
| |R1 = 1 | 10 | 1 | 0 | 0 | 0 |
| |R2 = R0 | 10 | 1 | 0 | 0 | 0 |
| |R2 += R1 | 10 | 1 | 1 | 0 | 0 |
| |R22 = R2 | 10 | 1 | 1 | 1 | 0 |
| |R33 += R2 | 10 | 1 | 1 | 1 | 1 |
| |R22 -= R1 | 10 | 1 | 1 | 0 | 1 |
| |IFZERO R22 GOTO 10 | 10 | 1 | 1 | 0 | 1 |
| |R33 -= R0 | 10 | 1 | 1 | 0 | 0 |
| |IFZERO R22 GOTO 10 | 10 | 1 | 1 | 0 | 0 |
| |R2 += R1 | 10 | 1 | 2 | 0 | 0 |
| |R22 = R2 | 10 | 1 | 2 | 2 | 0 |
| |R33 += R2 | 10 | 1 | 2 | 2 | 2 |
| |R22 -= R1 | 10 | 1 | 2 | 1 | 2 |
| |IFZERO R22 GOTO 10 | 10 | 1 | 2 | 1 | 2 |
| |GOTO 6 | 10 | 1 | 2 | 1 | 2 |
| |R33 += R2 | 10 | 1 | 2 | 1 | 4 |
| |R22 -= R1 | 10 | 1 | 2 | 0 | 4 |
| |IFZERO R22 GOTO 10 | 10 | 1 | 2 | 0 | 4 |
| |R33 -= R0 | 10 | 1 | 2 | 0 | 0 |
| |IFZERO R22 GOTO 10 | 10 | 1 | 2 | 0 | 0 |
| |R2 += R1 | 10 | 1 | 3 | 0 | 0 |
| |R22 = R2 | 10 | 1 | 3 | 3 | 0 |
| |R33 += R2 | 10 | 1 | 3 | 3 | 3 |
| |R22 -= R1 | 10 | 1 | 3 | 2 | 3 |
| |IFZERO R22 GOTO 10 | 10 | 1 | 3 | 2 | 3 |
| |GOTO 6 | 10 | 1 | 3 | 2 | 3 |
| |R33 += R2 | 10 | 1 | 3 | 2 | 6 |
| |R22 -= R1 | 10 | 1 | 3 | 1 | 6 |
| |IFZERO R22 GOTO 10 | 10 | 1 | 3 | 1 | 6 |
| |GOTO 6 | 10 | 1 | 3 | 1 | 6 |
| |R33 += R2 | 10 | 1 | 3 | 1 | 9 |
| |R22 -= R1 | 10 | 1 | 3 | 0 | 9 |
| |IFZERO R22 GOTO 10 | 10 | 1 | 3 | 0 | 9 |
| |R33 -= R0 | 10 | 1 | 3 | 0 | 0 |
| |IFZERO R22 GOTO 10 | 10 | 1 | 3 | 0 | 0 |
| |R2 += R1 | 10 | 1 | 4 | 0 | 0 |
| |R22 = R2 | 10 | 1 | 4 | 4 | 0 |
| |R33 += R2 | 10 | 1 | 4 | 4 | 4 |
| |R22 -= R1 | 10 | 1 | 4 | 3 | 4 |
| |IFZERO R22 GOTO 10 | 10 | 1 | 4 | 3 | 4 |
| |GOTO 6 | 10 | 1 | 4 | 3 | 4 |
| |R33 += R2 | 10 | 1 | 4 | 3 | 8 |
| |R22 -= R1 | 10 | 1 | 4 | 2 | 8 |
| |IFZERO R22 GOTO 10 | 10 | 1 | 4 | 2 | 8 |
| |GOTO 6 | 10 | 1 | 4 | 2 | 8 |
| |R33 += R2 | 10 | 1 | 4 | 2 | 12 |
| |R22 -= R1 | 10 | 1 | 4 | 1 | 12 |
| |IFZERO R22 GOTO 10 | 10 | 1 | 4 | 1 | 12 |
| |GOTO 6 | 10 | 1 | 4 | 1 | 12 |
| |R33 += R2 | 10 | 1 | 4 | 1 | 16 |
| |R22 -= R1 | 10 | 1 | 4 | 0 | 16 |
| |IFZERO R22 GOTO 10 | 10 | 1 | 4 | 0 | 16 |
| |R33 -= R0 | 10 | 1 | 4 | 0 | 6 |
| |IFZERO R22 GOTO 10 | 10 | 1 | 4 | 0 | 6 |
| |R2 -= R1 | 10 | 1 | 3 | 0 | 6 |
| |R0 = R2 | 3 | 1 | 3 | 0 | 6 |
Beispiel für n = 16
| Anweisung | R0 | R1 | R1 | R22 | R33 |
|---|---|---|---|---|---|
| |R0 = n | 16 | 0 | 0 | 0 | 0 |
| |R1 = 1 | 16 | 1 | 0 | 0 | 0 |
| |R2 = R0 | 16 | 1 | 0 | 0 | 0 |
| |R2 += R1 | 16 | 1 | 1 | 0 | 0 |
| |R22 = R2 | 16 | 1 | 1 | 1 | 0 |
| |R33 += R2 | 16 | 1 | 1 | 1 | 1 |
| |R22 -= R1 | 16 | 1 | 1 | 0 | 1 |
| |IFZERO R22 GOTO 10 | 16 | 1 | 1 | 0 | 1 |
| |R33 -= R0 | 16 | 1 | 1 | 0 | 0 |
| |IFZERO R22 GOTO 10 | 16 | 1 | 1 | 0 | 0 |
| |R2 += R1 | 16 | 1 | 2 | 0 | 0 |
| |R22 = R2 | 16 | 1 | 2 | 2 | 0 |
| |R33 += R2 | 16 | 1 | 2 | 2 | 2 |
| |R22 -= R1 | 16 | 1 | 2 | 1 | 2 |
| |IFZERO R22 GOTO 10 | 16 | 1 | 2 | 1 | 2 |
| |GOTO 6 | 16 | 1 | 2 | 1 | 2 |
| |R33 += R2 | 16 | 1 | 2 | 1 | 4 |
| |R22 -= R1 | 16 | 1 | 2 | 0 | 4 |
| |IFZERO R22 GOTO 10 | 16 | 1 | 2 | 0 | 4 |
| |R33 -= R0 | 16 | 1 | 2 | 0 | 0 |
| |IFZERO R22 GOTO 10 | 16 | 1 | 2 | 0 | 0 |
| |R2 += R1 | 16 | 1 | 3 | 0 | 0 |
| |R22 = R2 | 16 | 1 | 3 | 3 | 0 |
| |R33 += R2 | 16 | 1 | 3 | 3 | 3 |
| |R22 -= R1 | 16 | 1 | 3 | 2 | 3 |
| |IFZERO R22 GOTO 10 | 16 | 1 | 3 | 2 | 3 |
| |GOTO 6 | 16 | 1 | 3 | 2 | 3 |
| |R33 += R2 | 16 | 1 | 3 | 2 | 6 |
| |R22 -= R1 | 16 | 1 | 3 | 1 | 6 |
| |IFZERO R22 GOTO 10 | 16 | 1 | 3 | 1 | 6 |
| |GOTO 6 | 16 | 1 | 3 | 1 | 6 |
| |R33 += R2 | 16 | 1 | 3 | 1 | 9 |
| |R22 -= R1 | 16 | 1 | 3 | 0 | 9 |
| |IFZERO R22 GOTO 10 | 16 | 1 | 3 | 0 | 9 |
| |R33 -= R0 | 16 | 1 | 3 | 0 | 0 |
| |IFZERO R22 GOTO 10 | 16 | 1 | 3 | 0 | 0 |
| |R2 += R1 | 16 | 1 | 4 | 0 | 0 |
| |R22 = R2 | 16 | 1 | 4 | 4 | 0 |
| |R33 += R2 | 16 | 1 | 4 | 4 | 4 |
| |R22 -= R1 | 16 | 1 | 4 | 3 | 4 |
| |IFZERO R22 GOTO 10 | 16 | 1 | 4 | 3 | 4 |
| |GOTO 6 | 16 | 1 | 4 | 3 | 4 |
| |R33 += R2 | 16 | 1 | 4 | 3 | 8 |
| |R22 -= R1 | 16 | 1 | 4 | 2 | 8 |
| |IFZERO R22 GOTO 10 | 16 | 1 | 4 | 2 | 8 |
| |GOTO 6 | 16 | 1 | 4 | 2 | 8 |
| |R33 += R2 | 16 | 1 | 4 | 2 | 12 |
| |R22 -= R1 | 16 | 1 | 4 | 1 | 12 |
| |IFZERO R22 GOTO 10 | 16 | 1 | 4 | 1 | 12 |
| |GOTO 6 | 16 | 1 | 4 | 1 | 12 |
| |R33 += R2 | 16 | 1 | 4 | 1 | 16 |
| |R22 -= R1 | 16 | 1 | 4 | 0 | 16 |
| |IFZERO R22 GOTO 10 | 16 | 1 | 4 | 0 | 16 |
| |R33 -= R0 | 16 | 1 | 4 | 0 | 0 |
| |IFZERO R22 GOTO 10 | 16 | 1 | 4 | 0 | 0 |
| |R2 += R1 | 16 | 1 | 5 | 0 | 0 |
| |R22 = R2 | 16 | 1 | 5 | 5 | 0 |
| |R33 += R2 | 16 | 1 | 5 | 5 | 5 |
| |R22 -= R1 | 16 | 1 | 5 | 4 | 5 |
| |IFZERO R22 GOTO 10 | 16 | 1 | 5 | 4 | 5 |
| |GOTO 6 | 16 | 1 | 5 | 4 | 5 |
| |R33 += R2 | 16 | 1 | 5 | 4 | 10 |
| |R22 -= R1 | 16 | 1 | 5 | 3 | 10 |
| |IFZERO R22 GOTO 10 | 16 | 1 | 5 | 3 | 10 |
| |GOTO 6 | 16 | 1 | 5 | 3 | 10 |
| |R33 += R2 | 16 | 1 | 5 | 3 | 15 |
| |R22 -= R1 | 16 | 1 | 5 | 2 | 15 |
| |IFZERO R22 GOTO 10 | 16 | 1 | 5 | 2 | 15 |
| |GOTO 6 | 16 | 1 | 5 | 2 | 15 |
| |R33 += R2 | 16 | 1 | 5 | 2 | 20 |
| |R22 -= R1 | 16 | 1 | 5 | 1 | 20 |
| |IFZERO R22 GOTO 10 | 16 | 1 | 5 | 1 | 20 |
| |GOTO 6 | 16 | 1 | 5 | 1 | 20 |
| |R33 += R2 | 16 | 1 | 5 | 1 | 25 |
| |R22 -= R1 | 16 | 1 | 5 | 0 | 25 |
| |IFZERO R22 GOTO 10 | 16 | 1 | 5 | 0 | 25 |
| |R33 -= R0 | 16 | 1 | 5 | 0 | 9 |
| |IFZERO R22 GOTO 10 | 16 | 1 | 5 | 0 | 9 |
| |R2 -= R1 | 16 | 1 | 4 | 0 | 9 |
| |R0 = R2 | 4 | 1 | 4 | 0 | 9 |
Beispiel für n = 77
| Anweisung | R0 | R1 | R1 | R22 | R33 |
|---|---|---|---|---|---|
| |R0 = n | 77 | 0 | 0 | 0 | 0 |
| |R1 = 1 | 77 | 1 | 0 | 0 | 0 |
| |R2 = R0 | 77 | 1 | 0 | 0 | 0 |
| |R2 += R1 | 77 | 1 | 1 | 0 | 0 |
| |R22 = R2 | 77 | 1 | 1 | 1 | 0 |
| |R33 += R2 | 77 | 1 | 1 | 1 | 1 |
| |R22 -= R1 | 77 | 1 | 1 | 0 | 1 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 1 | 0 | 1 |
| |R33 -= R0 | 77 | 1 | 1 | 0 | 0 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 1 | 0 | 0 |
| |R2 += R1 | 77 | 1 | 2 | 0 | 0 |
| |R22 = R2 | 77 | 1 | 2 | 2 | 0 |
| |R33 += R2 | 77 | 1 | 2 | 2 | 2 |
| |R22 -= R1 | 77 | 1 | 2 | 1 | 2 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 2 | 1 | 2 |
| |GOTO 6 | 77 | 1 | 2 | 1 | 2 |
| |R33 += R2 | 77 | 1 | 2 | 1 | 4 |
| |R22 -= R1 | 77 | 1 | 2 | 0 | 4 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 2 | 0 | 4 |
| |R33 -= R0 | 77 | 1 | 2 | 0 | 0 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 2 | 0 | 0 |
| |R2 += R1 | 77 | 1 | 3 | 0 | 0 |
| |R22 = R2 | 77 | 1 | 3 | 3 | 0 |
| |R33 += R2 | 77 | 1 | 3 | 3 | 3 |
| |R22 -= R1 | 77 | 1 | 3 | 2 | 3 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 3 | 2 | 3 |
| |GOTO 6 | 77 | 1 | 3 | 2 | 3 |
| |R33 += R2 | 77 | 1 | 3 | 2 | 6 |
| |R22 -= R1 | 77 | 1 | 3 | 1 | 6 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 3 | 1 | 6 |
| |GOTO 6 | 77 | 1 | 3 | 1 | 6 |
| |R33 += R2 | 77 | 1 | 3 | 1 | 9 |
| |R22 -= R1 | 77 | 1 | 3 | 0 | 9 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 3 | 0 | 9 |
| |R33 -= R0 | 77 | 1 | 3 | 0 | 0 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 3 | 0 | 0 |
| |R2 += R1 | 77 | 1 | 4 | 0 | 0 |
| |R22 = R2 | 77 | 1 | 4 | 4 | 0 |
| |R33 += R2 | 77 | 1 | 4 | 4 | 4 |
| |R22 -= R1 | 77 | 1 | 4 | 3 | 4 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 4 | 3 | 4 |
| |GOTO 6 | 77 | 1 | 4 | 3 | 4 |
| |R33 += R2 | 77 | 1 | 4 | 3 | 8 |
| |R22 -= R1 | 77 | 1 | 4 | 2 | 8 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 4 | 2 | 8 |
| |GOTO 6 | 77 | 1 | 4 | 2 | 8 |
| |R33 += R2 | 77 | 1 | 4 | 2 | 12 |
| |R22 -= R1 | 77 | 1 | 4 | 1 | 12 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 4 | 1 | 12 |
| |GOTO 6 | 77 | 1 | 4 | 1 | 12 |
| |R33 += R2 | 77 | 1 | 4 | 1 | 16 |
| |R22 -= R1 | 77 | 1 | 4 | 0 | 16 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 4 | 0 | 16 |
| |R33 -= R0 | 77 | 1 | 4 | 0 | 0 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 4 | 0 | 0 |
| |R2 += R1 | 77 | 1 | 5 | 0 | 0 |
| |R22 = R2 | 77 | 1 | 5 | 5 | 0 |
| |R33 += R2 | 77 | 1 | 5 | 5 | 5 |
| |R22 -= R1 | 77 | 1 | 5 | 4 | 5 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 5 | 4 | 5 |
| |GOTO 6 | 77 | 1 | 5 | 4 | 5 |
| |R33 += R2 | 77 | 1 | 5 | 4 | 10 |
| |R22 -= R1 | 77 | 1 | 5 | 3 | 10 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 5 | 3 | 10 |
| |GOTO 6 | 77 | 1 | 5 | 3 | 10 |
| |R33 += R2 | 77 | 1 | 5 | 3 | 15 |
| |R22 -= R1 | 77 | 1 | 5 | 2 | 15 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 5 | 2 | 15 |
| |GOTO 6 | 77 | 1 | 5 | 2 | 15 |
| |R33 += R2 | 77 | 1 | 5 | 2 | 20 |
| |R22 -= R1 | 77 | 1 | 5 | 1 | 20 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 5 | 1 | 20 |
| |GOTO 6 | 77 | 1 | 5 | 1 | 20 |
| |R33 += R2 | 77 | 1 | 5 | 1 | 25 |
| |R22 -= R1 | 77 | 1 | 5 | 0 | 25 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 5 | 0 | 25 |
| |R33 -= R0 | 77 | 1 | 5 | 0 | 0 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 5 | 0 | 0 |
| |R2 += R1 | 77 | 1 | 6 | 0 | 0 |
| |R22 = R2 | 77 | 1 | 6 | 6 | 0 |
| |R33 += R2 | 77 | 1 | 6 | 6 | 6 |
| |R22 -= R1 | 77 | 1 | 6 | 5 | 6 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 6 | 5 | 6 |
| |GOTO 6 | 77 | 1 | 6 | 5 | 6 |
| |R33 += R2 | 77 | 1 | 6 | 5 | 12 |
| |R22 -= R1 | 77 | 1 | 6 | 4 | 12 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 6 | 4 | 12 |
| |GOTO 6 | 77 | 1 | 6 | 4 | 12 |
| |R33 += R2 | 77 | 1 | 6 | 4 | 18 |
| |R22 -= R1 | 77 | 1 | 6 | 3 | 18 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 6 | 3 | 18 |
| |GOTO 6 | 77 | 1 | 6 | 3 | 18 |
| |R33 += R2 | 77 | 1 | 6 | 3 | 24 |
| |R22 -= R1 | 77 | 1 | 6 | 2 | 24 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 6 | 2 | 24 |
| |GOTO 6 | 77 | 1 | 6 | 2 | 24 |
| |R33 += R2 | 77 | 1 | 6 | 2 | 30 |
| |R22 -= R1 | 77 | 1 | 6 | 1 | 30 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 6 | 1 | 30 |
| |GOTO 6 | 77 | 1 | 6 | 1 | 30 |
| |R33 += R2 | 77 | 1 | 6 | 1 | 36 |
| |R22 -= R1 | 77 | 1 | 6 | 0 | 36 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 6 | 0 | 36 |
| |R33 -= R0 | 77 | 1 | 6 | 0 | 0 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 6 | 0 | 0 |
| |R2 += R1 | 77 | 1 | 7 | 0 | 0 |
| |R22 = R2 | 77 | 1 | 7 | 7 | 0 |
| |R33 += R2 | 77 | 1 | 7 | 7 | 7 |
| |R22 -= R1 | 77 | 1 | 7 | 6 | 7 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 7 | 6 | 7 |
| |GOTO 6 | 77 | 1 | 7 | 6 | 7 |
| |R33 += R2 | 77 | 1 | 7 | 6 | 14 |
| |R22 -= R1 | 77 | 1 | 7 | 5 | 14 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 7 | 5 | 14 |
| |GOTO 6 | 77 | 1 | 7 | 5 | 14 |
| |R33 += R2 | 77 | 1 | 7 | 5 | 21 |
| |R22 -= R1 | 77 | 1 | 7 | 4 | 21 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 7 | 4 | 21 |
| |GOTO 6 | 77 | 1 | 7 | 4 | 21 |
| |R33 += R2 | 77 | 1 | 7 | 4 | 28 |
| |R22 -= R1 | 77 | 1 | 7 | 3 | 28 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 7 | 3 | 28 |
| |GOTO 6 | 77 | 1 | 7 | 3 | 28 |
| |R33 += R2 | 77 | 1 | 7 | 3 | 35 |
| |R22 -= R1 | 77 | 1 | 7 | 2 | 35 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 7 | 2 | 35 |
| |GOTO 6 | 77 | 1 | 7 | 2 | 35 |
| |R33 += R2 | 77 | 1 | 7 | 2 | 42 |
| |R22 -= R1 | 77 | 1 | 7 | 1 | 42 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 7 | 1 | 42 |
| |GOTO 6 | 77 | 1 | 7 | 1 | 42 |
| |R33 += R2 | 77 | 1 | 7 | 1 | 49 |
| |R22 -= R1 | 77 | 1 | 7 | 0 | 49 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 7 | 0 | 49 |
| |R33 -= R0 | 77 | 1 | 7 | 0 | 0 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 7 | 0 | 0 |
| |R2 += R1 | 77 | 1 | 8 | 0 | 0 |
| |R22 = R2 | 77 | 1 | 8 | 8 | 0 |
| |R33 += R2 | 77 | 1 | 8 | 8 | 8 |
| |R22 -= R1 | 77 | 1 | 8 | 7 | 8 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 8 | 7 | 8 |
| |GOTO 6 | 77 | 1 | 8 | 7 | 8 |
| |R33 += R2 | 77 | 1 | 8 | 7 | 16 |
| |R22 -= R1 | 77 | 1 | 8 | 6 | 16 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 8 | 6 | 16 |
| |GOTO 6 | 77 | 1 | 8 | 6 | 16 |
| |R33 += R2 | 77 | 1 | 8 | 6 | 24 |
| |R22 -= R1 | 77 | 1 | 8 | 5 | 24 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 8 | 5 | 24 |
| |GOTO 6 | 77 | 1 | 8 | 5 | 24 |
| |R33 += R2 | 77 | 1 | 8 | 5 | 32 |
| |R22 -= R1 | 77 | 1 | 8 | 4 | 32 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 8 | 4 | 32 |
| |GOTO 6 | 77 | 1 | 8 | 4 | 32 |
| |R33 += R2 | 77 | 1 | 8 | 4 | 40 |
| |R22 -= R1 | 77 | 1 | 8 | 3 | 40 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 8 | 3 | 40 |
| |GOTO 6 | 77 | 1 | 8 | 3 | 40 |
| |R33 += R2 | 77 | 1 | 8 | 3 | 48 |
| |R22 -= R1 | 77 | 1 | 8 | 2 | 48 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 8 | 2 | 48 |
| |GOTO 6 | 77 | 1 | 8 | 2 | 48 |
| |R33 += R2 | 77 | 1 | 8 | 2 | 56 |
| |R22 -= R1 | 77 | 1 | 8 | 1 | 56 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 8 | 1 | 56 |
| |GOTO 6 | 77 | 1 | 8 | 1 | 56 |
| |R33 += R2 | 77 | 1 | 8 | 1 | 64 |
| |R22 -= R1 | 77 | 1 | 8 | 0 | 64 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 8 | 0 | 64 |
| |R33 -= R0 | 77 | 1 | 8 | 0 | 0 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 8 | 0 | 0 |
| |R2 += R1 | 77 | 1 | 9 | 0 | 0 |
| |R22 = R2 | 77 | 1 | 9 | 9 | 0 |
| |R33 += R2 | 77 | 1 | 9 | 9 | 9 |
| |R22 -= R1 | 77 | 1 | 9 | 8 | 9 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 9 | 8 | 9 |
| |GOTO 6 | 77 | 1 | 9 | 8 | 9 |
| |R33 += R2 | 77 | 1 | 9 | 8 | 18 |
| |R22 -= R1 | 77 | 1 | 9 | 7 | 18 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 9 | 7 | 18 |
| |GOTO 6 | 77 | 1 | 9 | 7 | 18 |
| |R33 += R2 | 77 | 1 | 9 | 7 | 27 |
| |R22 -= R1 | 77 | 1 | 9 | 6 | 27 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 9 | 6 | 27 |
| |GOTO 6 | 77 | 1 | 9 | 6 | 27 |
| |R33 += R2 | 77 | 1 | 9 | 6 | 36 |
| |R22 -= R1 | 77 | 1 | 9 | 5 | 36 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 9 | 5 | 36 |
| |GOTO 6 | 77 | 1 | 9 | 5 | 36 |
| |R33 += R2 | 77 | 1 | 9 | 5 | 45 |
| |R22 -= R1 | 77 | 1 | 9 | 4 | 45 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 9 | 4 | 45 |
| |GOTO 6 | 77 | 1 | 9 | 4 | 45 |
| |R33 += R2 | 77 | 1 | 9 | 4 | 54 |
| |R22 -= R1 | 77 | 1 | 9 | 3 | 54 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 9 | 3 | 54 |
| |GOTO 6 | 77 | 1 | 9 | 3 | 54 |
| |R33 += R2 | 77 | 1 | 9 | 3 | 63 |
| |R22 -= R1 | 77 | 1 | 9 | 2 | 63 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 9 | 2 | 63 |
| |GOTO 6 | 77 | 1 | 9 | 2 | 63 |
| |R33 += R2 | 77 | 1 | 9 | 2 | 72 |
| |R22 -= R1 | 77 | 1 | 9 | 1 | 72 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 9 | 1 | 72 |
| |GOTO 6 | 77 | 1 | 9 | 1 | 72 |
| |R33 += R2 | 77 | 1 | 9 | 1 | 81 |
| |R22 -= R1 | 77 | 1 | 9 | 0 | 81 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 9 | 0 | 81 |
| |R33 -= R0 | 77 | 1 | 9 | 0 | 4 |
| |IFZERO R22 GOTO 10 | 77 | 1 | 9 | 0 | 4 |
| |R2 -= R1 | 77 | 1 | 8 | 0 | 4 |
| |R0 = R2 | 8 | 1 | 8 | 0 | 4 |
RAM zur Ermittlung des größten gemeinsamen Teilers (ggt) - Euklidischer Algorithmus
| Befehlszähler | Anweisung | Bemerkung |
|---|---|---|
| | 0 | R0 = a | belegen von R0 mit der ersten natürlichen Zahl a |
| | 1 | R1 = b | belegen von R1 mit der ersten natürlichen Zahl b |
| | 2 | IFZERO R1 GOTO 12 | Sprung zu 12 da R0 das Ergebnis beinhaltet |
| | 3 | IFZERO R0 GOTO 11 | Sprung zu 11 da R1 das Ergebnis beinhaltet |
| | 4 | R2 = R0 | Zwischenspeichern von R0 in R2 für Größer vergleich |
| | 5 | R2 -= R1 | R1 von R2 subtrahieren für Größer vergleich |
| | 6 | IFZERO R2 GOTO 9 | wenn R2 0 ist, ist R1 > R0 |
| | 7 | R0 -= R1 | R1 von R0 subtrahieren |
| | 8 | GOTO 2 | Sprung zum Schleifenanfang |
| | 9 | R1 -= R0 | R0 von R1 subtrahieren |
| | 10 | GOTO 2 | Sprung zum Schleifenanfang |
| | 11 | R0 = R1 | Ergebnis in R0 schreiben |
| | 12 | STOP |
Beispiel mit a = 2 und b = 4
| Anweisung | R0 | R1 | R1 |
|---|---|---|---|
| |R0 = a | 2 | 0 | 0 |
| |R1 = b | 2 | 4 | 0 |
| |IFZERO R1 GOTO 12 | 2 | 4 | 0 |
| |IFZERO R0 GOTO 11 | 2 | 4 | 0 |
| |R2 = R0 | 2 | 4 | 2 |
| |R2 -= R1 | 2 | 4 | 0 |
| |IFZERO R2 GOTO 11 | 2 | 4 | 0 |
| |R1 -= R0 | 2 | 2 | 0 |
| |GOTO 2 | 2 | 2 | 0 |
| |IFZERO R1 GOTO 12 | 2 | 2 | 0 |
| |IFZERO R0 GOTO 11 | 2 | 2 | 0 |
| |R2 = R0 | 2 | 2 | 2 |
| |R2 -= R1 | 2 | 2 | 0 |
| |IFZERO R2 GOTO 11 | 2 | 2 | 0 |
| |R1 -= R0 | 2 | 0 | 0 |
| |GOTO 2 | 2 | 0 | 0 |
| |IFZERO R1 GOTO 12 | 2 | 0 | 0 |
Beispiel mit a = 2 und b = 15
| Anweisung | R0 | R1 | R1 |
|---|---|---|---|
| |R0 = a | 2 | 0 | 0 |
| |R1 = b | 2 | 15 | 0 |
| |IFZERO R1 GOTO 12 | 2 | 15 | 0 |
| |IFZERO R0 GOTO 11 | 2 | 15 | 0 |
| |R2 = R0 | 2 | 15 | 2 |
| |R2 -= R1 | 2 | 15 | 0 |
| |IFZERO R2 GOTO 11 | 2 | 15 | 0 |
| |R1 -= R0 | 2 | 13 | 0 |
| |GOTO 2 | 2 | 13 | 0 |
| |IFZERO R1 GOTO 12 | 2 | 13 | 0 |
| |IFZERO R0 GOTO 11 | 2 | 13 | 0 |
| |R2 = R0 | 2 | 13 | 2 |
| |R2 -= R1 | 2 | 13 | 0 |
| |IFZERO R2 GOTO 11 | 2 | 13 | 0 |
| |R1 -= R0 | 2 | 11 | 0 |
| |GOTO 2 | 2 | 11 | 0 |
| |IFZERO R1 GOTO 12 | 2 | 11 | 0 |
| |IFZERO R0 GOTO 11 | 2 | 11 | 0 |
| |R2 = R0 | 2 | 11 | 2 |
| |R2 -= R1 | 2 | 11 | 0 |
| |IFZERO R2 GOTO 11 | 2 | 11 | 0 |
| |R1 -= R0 | 2 | 9 | 0 |
| |GOTO 2 | 2 | 9 | 0 |
| |IFZERO R1 GOTO 12 | 2 | 9 | 0 |
| |IFZERO R0 GOTO 11 | 2 | 9 | 0 |
| |R2 = R0 | 2 | 9 | 2 |
| |R2 -= R1 | 2 | 9 | 0 |
| |IFZERO R2 GOTO 11 | 2 | 9 | 0 |
| |R1 -= R0 | 2 | 7 | 0 |
| |GOTO 2 | 2 | 7 | 0 |
| |IFZERO R1 GOTO 12 | 2 | 7 | 0 |
| |IFZERO R0 GOTO 11 | 2 | 7 | 0 |
| |R2 = R0 | 2 | 7 | 2 |
| |R2 -= R1 | 2 | 7 | 0 |
| |IFZERO R2 GOTO 11 | 2 | 7 | 0 |
| |R1 -= R0 | 2 | 5 | 0 |
| |GOTO 2 | 2 | 5 | 0 |
| |IFZERO R1 GOTO 12 | 2 | 5 | 0 |
| |IFZERO R0 GOTO 11 | 2 | 5 | 0 |
| |R2 = R0 | 2 | 5 | 2 |
| |R2 -= R1 | 2 | 5 | 0 |
| |IFZERO R2 GOTO 11 | 2 | 5 | 0 |
| |R1 -= R0 | 2 | 3 | 0 |
| |GOTO 2 | 2 | 3 | 0 |
| |IFZERO R1 GOTO 12 | 2 | 3 | 0 |
| |IFZERO R0 GOTO 11 | 2 | 3 | 0 |
| |R2 = R0 | 2 | 3 | 2 |
| |R2 -= R1 | 2 | 3 | 0 |
| |IFZERO R2 GOTO 11 | 2 | 3 | 0 |
| |R1 -= R0 | 2 | 1 | 0 |
| |GOTO 2 | 2 | 1 | 0 |
| |IFZERO R1 GOTO 12 | 2 | 1 | 0 |
| |IFZERO R0 GOTO 11 | 2 | 1 | 0 |
| |R2 = R0 | 2 | 1 | 2 |
| |R2 -= R1 | 2 | 1 | 1 |
| |IFZERO R2 GOTO 11 | 2 | 1 | 1 |
| |R0 -= R1 | 1 | 1 | 1 |
| |GOTO 2 | 1 | 1 | 1 |
| |IFZERO R1 GOTO 12 | 1 | 1 | 1 |
| |IFZERO R0 GOTO 11 | 1 | 1 | 1 |
| |R2 = R0 | 1 | 1 | 1 |
| |R2 -= R1 | 1 | 1 | 0 |
| |IFZERO R2 GOTO 11 | 1 | 1 | 0 |
| |R1 -= R0 | 1 | 0 | 0 |
| |GOTO 2 | 1 | 0 | 0 |
| |IFZERO R1 GOTO 12 | 1 | 0 | 0 |
Beispiel mit a = 119 und b = 7
| Anweisung | R0 | R1 | R1 |
|---|---|---|---|
| |R0 = a | 119 | 0 | 0 |
| |R1 = b | 119 | 7 | 0 |
| |IFZERO R1 GOTO 12 | 119 | 7 | 0 |
| |IFZERO R0 GOTO 11 | 119 | 7 | 0 |
| |R2 = R0 | 119 | 7 | 119 |
| |R2 -= R1 | 119 | 7 | 112 |
| |IFZERO R2 GOTO 11 | 119 | 7 | 112 |
| |R0 -= R1 | 112 | 7 | 112 |
| |GOTO 2 | 112 | 7 | 112 |
| |IFZERO R1 GOTO 12 | 112 | 7 | 112 |
| |IFZERO R0 GOTO 11 | 112 | 7 | 112 |
| |R2 = R0 | 112 | 7 | 112 |
| |R2 -= R1 | 112 | 7 | 105 |
| |IFZERO R2 GOTO 11 | 112 | 7 | 105 |
| |R0 -= R1 | 105 | 7 | 105 |
| |GOTO 2 | 105 | 7 | 105 |
| |IFZERO R1 GOTO 12 | 105 | 7 | 105 |
| |IFZERO R0 GOTO 11 | 105 | 7 | 105 |
| |R2 = R0 | 105 | 7 | 105 |
| |R2 -= R1 | 105 | 7 | 98 |
| |IFZERO R2 GOTO 11 | 105 | 7 | 98 |
| |R0 -= R1 | 98 | 7 | 98 |
| |GOTO 2 | 98 | 7 | 98 |
| |IFZERO R1 GOTO 12 | 98 | 7 | 98 |
| |IFZERO R0 GOTO 11 | 98 | 7 | 98 |
| |R2 = R0 | 98 | 7 | 98 |
| |R2 -= R1 | 98 | 7 | 91 |
| |IFZERO R2 GOTO 11 | 98 | 7 | 91 |
| |R0 -= R1 | 91 | 7 | 91 |
| |GOTO 2 | 91 | 7 | 91 |
| |IFZERO R1 GOTO 12 | 91 | 7 | 91 |
| |IFZERO R0 GOTO 11 | 91 | 7 | 91 |
| |R2 = R0 | 91 | 7 | 91 |
| |R2 -= R1 | 91 | 7 | 84 |
| |IFZERO R2 GOTO 11 | 91 | 7 | 84 |
| |R0 -= R1 | 84 | 7 | 84 |
| |GOTO 2 | 84 | 7 | 84 |
| |IFZERO R1 GOTO 12 | 84 | 7 | 84 |
| |IFZERO R0 GOTO 11 | 84 | 7 | 84 |
| |R2 = R0 | 84 | 7 | 84 |
| |R2 -= R1 | 84 | 7 | 77 |
| |IFZERO R2 GOTO 11 | 84 | 7 | 77 |
| |R0 -= R1 | 77 | 7 | 77 |
| |GOTO 2 | 77 | 7 | 77 |
| |IFZERO R1 GOTO 12 | 77 | 7 | 77 |
| |IFZERO R0 GOTO 11 | 77 | 7 | 77 |
| |R2 = R0 | 77 | 7 | 77 |
| |R2 -= R1 | 77 | 7 | 70 |
| |IFZERO R2 GOTO 11 | 77 | 7 | 70 |
| |R0 -= R1 | 70 | 7 | 70 |
| |GOTO 2 | 70 | 7 | 70 |
| |IFZERO R1 GOTO 12 | 70 | 7 | 70 |
| |IFZERO R0 GOTO 11 | 70 | 7 | 70 |
| |R2 = R0 | 70 | 7 | 70 |
| |R2 -= R1 | 70 | 7 | 63 |
| |IFZERO R2 GOTO 11 | 70 | 7 | 63 |
| |R0 -= R1 | 63 | 7 | 63 |
| |GOTO 2 | 63 | 7 | 63 |
| |IFZERO R1 GOTO 12 | 63 | 7 | 63 |
| |IFZERO R0 GOTO 11 | 63 | 7 | 63 |
| |R2 = R0 | 63 | 7 | 63 |
| |R2 -= R1 | 63 | 7 | 56 |
| |IFZERO R2 GOTO 11 | 63 | 7 | 56 |
| |R0 -= R1 | 56 | 7 | 56 |
| |GOTO 2 | 56 | 7 | 56 |
| |IFZERO R1 GOTO 12 | 56 | 7 | 56 |
| |IFZERO R0 GOTO 11 | 56 | 7 | 56 |
| |R2 = R0 | 56 | 7 | 56 |
| |R2 -= R1 | 56 | 7 | 49 |
| |IFZERO R2 GOTO 11 | 56 | 7 | 49 |
| |R0 -= R1 | 49 | 7 | 49 |
| |GOTO 2 | 49 | 7 | 49 |
| |IFZERO R1 GOTO 12 | 49 | 7 | 49 |
| |IFZERO R0 GOTO 11 | 49 | 7 | 49 |
| |R2 = R0 | 49 | 7 | 49 |
| |R2 -= R1 | 49 | 7 | 42 |
| |IFZERO R2 GOTO 11 | 49 | 7 | 42 |
| |R0 -= R1 | 42 | 7 | 42 |
| |GOTO 2 | 42 | 7 | 42 |
| |IFZERO R1 GOTO 12 | 42 | 7 | 42 |
| |IFZERO R0 GOTO 11 | 42 | 7 | 42 |
| |R2 = R0 | 42 | 7 | 42 |
| |R2 -= R1 | 42 | 7 | 35 |
| |IFZERO R2 GOTO 11 | 42 | 7 | 35 |
| |R0 -= R1 | 35 | 7 | 35 |
| |GOTO 2 | 35 | 7 | 35 |
| |IFZERO R1 GOTO 12 | 35 | 7 | 35 |
| |IFZERO R0 GOTO 11 | 35 | 7 | 35 |
| |R2 = R0 | 35 | 7 | 35 |
| |R2 -= R1 | 35 | 7 | 28 |
| |IFZERO R2 GOTO 11 | 35 | 7 | 28 |
| |R0 -= R1 | 28 | 7 | 28 |
| |GOTO 2 | 28 | 7 | 28 |
| |IFZERO R1 GOTO 12 | 28 | 7 | 28 |
| |IFZERO R0 GOTO 11 | 28 | 7 | 28 |
| |R2 = R0 | 28 | 7 | 28 |
| |R2 -= R1 | 28 | 7 | 21 |
| |IFZERO R2 GOTO 11 | 28 | 7 | 21 |
| |R0 -= R1 | 21 | 7 | 21 |
| |GOTO 2 | 21 | 7 | 21 |
| |IFZERO R1 GOTO 12 | 21 | 7 | 21 |
| |IFZERO R0 GOTO 11 | 21 | 7 | 21 |
| |R2 = R0 | 21 | 7 | 21 |
| |R2 -= R1 | 21 | 7 | 14 |
| |IFZERO R2 GOTO 11 | 21 | 7 | 14 |
| |R0 -= R1 | 14 | 7 | 14 |
| |GOTO 2 | 14 | 7 | 14 |
| |IFZERO R1 GOTO 12 | 14 | 7 | 14 |
| |IFZERO R0 GOTO 11 | 14 | 7 | 14 |
| |R2 = R0 | 14 | 7 | 14 |
| |R2 -= R1 | 14 | 7 | 7 |
| |IFZERO R2 GOTO 11 | 14 | 7 | 7 |
| |R0 -= R1 | 7 | 7 | 7 |
| |GOTO 2 | 7 | 7 | 7 |
| |IFZERO R1 GOTO 12 | 7 | 7 | 7 |
| |IFZERO R0 GOTO 11 | 7 | 7 | 7 |
| |R2 = R0 | 7 | 7 | 7 |
| |R2 -= R1 | 7 | 7 | 0 |
| |IFZERO R2 GOTO 11 | 7 | 7 | 0 |
| |R1 -= R0 | 7 | 0 | 0 |
| |GOTO 2 | 7 | 0 | 0 |
| |IFZERO R1 GOTO 12 | 7 | 0 | 0 |