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Zahlenformate

Zahlenformate. Dezimalzahlen. Basis = 10 (n k-1 n k-2 ...n 1 n 0 ) 10 = n k-1 • 10 k-1 + n k-2 • 10 k-2 + ... + n 1 • 10 + n 0 wobei 0 <= n i < 10 z.B.: 2345 10 = 2 • 10 3 + 3 • 10 2 + 4 • 10 + 5 = 2 • 1000 + 3 • 100 + 4 • 10 + 5 = 2000 + 300 + 40 + 5. Binärzahlen. Basis = 2

melyssa-newman
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Zahlenformate

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  1. Zahlenformate DVG1 - Zahlenformate

  2. Dezimalzahlen Basis = 10 (nk-1nk-2...n1n0)10 = nk-1 •10 k-1 + nk-2 •10 k-2 + ... + n1 •10 + n0 wobei 0 <= ni < 10 z.B.: 234510 = 2 • 10 3 + 3 • 10 2 + 4 • 10 + 5 = 2 • 1000 + 3 • 100+ 4 • 10 + 5 = 2000 + 300 + 40 + 5 DVG1 - Zahlenformate

  3. Binärzahlen Basis = 2 (nk-1nk-2...n1n0)2 = nk-1 •2 k-1 + nk-2 •2 k-2 + ... + n1 •2 + n0 wobei 0 <= ni < 2 z.B.: 1001012 = 1 • 2 5 + 0 • 2 4 + 0 • 2 3 + 1 • 2 2 + 0 • 2 + 1 = 1 • 32+ 0 • 16+ 0 • 8+ 1 • 4+ 0 • 2 + 1 = 32 + 4 + 1 = 3710 DVG1 - Zahlenformate

  4. Dezimalzahl ==> Binärzahl Gesucht Binärdarstellung einer Dezimalzahl D: D = nk-1 •2 k-1 + nk-2 •2 k-2 + ... + n1 •2 + n0 = (...((nk-1 •2 + nk-2 ) •2 + nk-3 ) •2 +...+ n1 ) •2 + n0 0 <= ni < 2 z.B.: 3910 = 19 •2 + 1 = (9 •2 + 1 ) •2 + 1 = ((4 •2 + 1 ) •2 + 1 ) •2 + 1 = (((2 •2 + 0 ) •2 + 1 ) •2 + 1 ) •2 + 1 = ((((1 •2 + 0 ) •2 + 0 ) •2 + 1 ) •2 + 1 ) •2 + 1 = 1001112 DVG1 - Zahlenformate

  5. Oktalzahlen Basis = 8 (nk-1nk-2...n1n0)8 = nk-1 •8 k-1 + nk-2 •8 k-2 + ... + n1 •8 + n0 wobei 0 <= ni < 8 z.B.: 76548 = 7 • 8 3 + 6 • 8 2 + 5 • 8 + 4 = 7 • 512+ 6 • 64+ 5 • 8 + 4 = 3584 + 384 + 40 +4 = 401210 DVG1 - Zahlenformate

  6. Dezimalzahl ==> Oktalzahl Gesucht Oktaldarstellung einer Dezimalzahl D: D = nk-1 •8 k-1 + nk-2 •8 k-2 + ... + n1 •8 + n0 = (...((nk-1 •8 + nk-2 ) •8 + nk-3 ) •8 +...+ n1 ) •8 + n0 0 <= ni < 8 z.B.: 401210 = 501 •8 + 4 = (62 •8 + 5 ) •8 + 4 = ((7 •8 + 6 ) •8 + 5 ) •8 + 4 = 76548 DVG1 - Zahlenformate

  7. Hexadezimalzahlen Basis = 16 (nk-1nk-2...n1n0)16 = nk-1 •16 k-1 + nk-2 •16 k-2 + ... + n1 •16 + n0 wobei 0 <= ni < 16 Ziffern: 0 . . . 9 A B C D E F A=10, B=11, C=12, D=13, E=14, F=15 z.B.: FEDC16 = 15 • 16 3 + 14 • 16 2 + 13 • 16 + 12 = 15 • 4096+ 14 • 256+ 13 • 16 + 12 = 61440 + 3584 + 208 + 12 = 6524410 DVG1 - Zahlenformate

  8. Dezimalzahl ==> Hexadezimalzahl Gesucht Hexadezimaldarstellung einer Dezimalzahl D: D = nk-1 •16 k-1 + nk-2 •16 k-2 + ... + n1 •16 + n0 = (...((nk-1 •16 + nk-2 ) •16 + nk-3 ) •16 +...+ n1 ) •16 + n0 0 <= ni < 16 z.B.: 6524410 = 4077 •16 + 12 = (254 •16 + 13 ) •16 + 12 = ((15 •16 + 14 ) •16 + 13 ) •16 + 12 = FEDC16 DVG1 - Zahlenformate

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