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Sistemidi numerazione

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modulo classi prime: rappresentazione digitale dei dati

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Sistemidi numerazione

  1. 1. Rappresentazione digitale dei dati Anna Rita Colella Modulo1: Concetti base Classe 1^ Informatica IT Zanon Udine a.s. 2014/2015
  2. 2. Un sistema di numerazione posizionale è un sistema in cui i simboli usati per scrivere i numeri (cifre) assumono valori diversi a seconda della posizione che occupano nella notazione. Anna Rita Colella Esempio: 518 è diverso da 158
  3. 3. Anna Rita Colella  Ogni numero intero N può essere scritto nella seguente forma: N=an*10n-1+ an-1*10n-2 + …+a2*101 +a1*100 Polinomio in cui ogni cifra viene rappresentata moltiplicandola per una potenza di 10 ak sono le cifre del numero N e 10 è la sua base 10k-1 è il peso ovvero la posizione che assume la cifra nel numero 518= 5*102 + 1*101 + 8*100 = 500+10+8 Sistema posizionale decimale
  4. 4. Sistema posizionale binario  Cifre: 0, 1  Base:2  Peso: potenze di 2  Ogni numero intero N può essere scritto nella seguente forma: N=an*2n-1+ an-1*2n-2 + …+a2*21 +a1*20 11010012 = 1*26 + 1*25 + 0*24 + 1*23 + 0*22 + 0*21 + 1*20 = 64+32+0+8+0+0+1 = 10510 Anna Rita Colella
  5. 5. Sistema posizionale esadecimale Anna Rita Colella  Cifre: 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F  Base:16  Peso: potenze di 16  Ogni numero intero N può essere scritto nella seguente forma: N=an*16n-1+ an-1*16n-2 + …+a2*161 +a1*160 2CA16 = 2*162 + 12*161 + 10*160 = 512 +192 +10= 71410
  6. 6. Esercizi Anna Rita Colella  Trasforma i seguenti numeri nel valore decimale:  101101  5AE  43D  1010111  0101011
  7. 7. Soluzioni in Excel Anna Rita Colella  Risolviamo gli esercizi con il foglio elettronico Excel Numero binario 101101 POSIZIONE 7 6 5 4 3 2 1 0 CIFRE 0 0 1 0 1 1 0 1 PESO 27 26 25 24 23 22 21 20 risultato in base 10 45 Numero esadecimale 3D4 POSIZIONE 7 6 5 4 3 2 1 0 CIFRE 3 D 4 CIFRE PER IL CALCOLO 0 0 0 0 0 3 13 4 PESO 167 166 165 164 163 162 161 160 risultato in base 10 980 CALCOLI CON NUMERI BINARI conversione da binario a decimale conversione da esadecimale a decimale
  8. 8. Conversioni da decimale a binario  Per convertire un numero da decimale a binario bisogna dividere il numero per due; si riportano il risultato e il resto finché il risultato diventa zero.  Il numero binario è dato dai resti ottenuti a partire dall’ultimo Anna Rita Colella
  9. 9. Soluzioni in Excel Anna Rita Colella  Risolviamo gli esercizi con il foglio elettronico Excel base da convertire 2 quoziente numero in base 10 45 45 resto 22 1 11 0 5 1 2 1 1 0 0 1 0 0 Numero decimale Numero binario (105)10 (1101001)2 (45)10 (101101)2 conversione da decimale a binario
  10. 10. Viaggio Nella Scienza - La Tecnologia e i computer Numeri binari e Computer Anna Rita Colella  Guarda questo filmato che spiega come il codice binario viene utilizzato per rappresentare le informazioni nel computer
  11. 11. Anna Rita Colella
  12. 12. Rappresentazione dell’informazione  I computer usano il sistema binario per rappresentare le informazioni  Questo avviene perché la corrente elettrica nei circuiti del computer può solo assumere due valori:  0 non c’è corrente  1 c’è corrente  Ogni cifra (zero, uno) viene chiamata bit (binary digit) Colella Anna Rita 12
  13. 13.  I bit normalmente sono considerati a gruppi di otto  Ogni gruppo di otto bit viene detto byte  Un gruppo di due byte viene detto word Colella Anna Rita 13
  14. 14. Bit e Byte Anna Rita Colella  Nel computer il byte è l’unità di misura dell’informazione e serve per misurare la capacità della memoria  Tutte le rappresentazioni numeriche adottate nei moderni calcolatori usano un numero di bit multiplo di 8  Poiché nel sistema binario ciascun valore corrisponde a una potenza di 2, i multipli del byte sono: - il Kilobyte (Kb): 2 in potenza di 10 ovvero 1024 byte; - il Megabyte (Mb): 2 in potenza di 20 ovvero 1.048.576 byte; - il Gigabyte (Gb): 2 in potenza di 30 ovvero 1.073.741.824 byte. 1 TeraByte = 1024 GigaBytes 1 PetaByte = 1024 TeraBytes 1 ExaByte = 1024 PetaBytes 1 ZettaByte = 1024 ExaBytes 1 YottaByte = 1024 ZettaBytes

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