restart;f:=x->exp(x);

NiM+SSJmRzYiZio2I0kieEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUkkZXhwR0YlNiM5JEYlRiVGJQ==

f5:=taylor(f(x),x=0,6);

NiM+SSNmNUc2IisxSSJ4R0YlIiIiIiIhRihGKCNGKCIiI0YrI0YoIiInIiIkI0YoIiNDIiIlI0YoIiQ/IiIiJi1JIk9HSSpwcm90ZWN0ZWRHRjc2I0YoRi0=

restglied:=coeftayl(f(x),x=1,6);

NiM+SSpyZXN0Z2xpZWRHNiIsJC1JJGV4cEc2JEkqcHJvdGVjdGVkR0YqSShfc3lzbGliR0YlNiMiIiIjRi0iJD8o

p:=unapply(convert(f5,polynom),x);

NiM+SSJwRzYiZio2I0kieEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLC4iIiJGLTkkRi0qJEYuIiIjI0YtRjAqJEYuIiIkI0YtIiInKiRGLiIiJSNGLSIjQyokRi4iIiYjRi0iJD8iRiVGJUYl

x0:=0;

NiM+SSN4MEc2IiIiIQ==

plot([f(x),p(x)],x=-2..4,color=[red,blue]);

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

x:=1;

NiM+SSJ4RzYiIiIi

approx:=evalf(p(x));

NiM+SSdhcHByb3hHNiIkIitubW07RiEiKg==

absfehler:=evalf(exp(1)-approx);

NiM+SSphYnNmZWhsZXJHNiIkIihoXmgiISIq

relfehler:=evalf((exp(1)-approx)/exp(1));

NiM+SSpyZWxmZWhsZXJHNiIkIitpXyU9JWYhIzg=

restglied:=evalf(restglied);

NiM+SSpyZXN0Z2xpZWRHNiIkIitHOVJ2UCEjNw==

restglied1:=evalf((exp(1)/(6)!)*(1-0)**6);

NiM+SStyZXN0Z2xpZWQxRzYiJCIrRzlSdlAhIzc=

vergleich:=evalf((restglied-absfehler)/restglied);

NiM+SSp2ZXJnbGVpY2hHNiIkIis3OSg9cyYhIzU=

f10:=taylor(f(x),x=0,11);

NiM+SSRmMTBHNiIrO0kieEdGJSIiIiIiIUYoRigjRigiIiNGKyNGKCIiJyIiJCNGKCIjQyIiJSNGKCIkPyIiIiYjRigiJD8oRi0jRigiJVNdIiIoI0YoIiY/LiUiIikjRigiJyEpR08iIiojRigiKCspR08iIzUtSSJPR0kqcHJvdGVjdGVkR0ZFNiNGKCIjNg==

restglied:=coeftayl(f(x),x=1,11);

NiM+SSpyZXN0Z2xpZWRHNiIsJC1JJGV4cEc2JEkqcHJvdGVjdGVkR0YqSShfc3lzbGliR0YlNiMiIiIjRi0iKStvIipS

p:=unapply(convert(f10,polynom),x);

NiM+SSJwRzYiZio2I0kieEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLDgiIiJGLTkkRi0qJEYuIiIjI0YtRjAqJEYuIiIkI0YtIiInKiRGLiIiJSNGLSIjQyokRi4iIiYjRi0iJD8iKiRGLkY1I0YtIiQ/KCokRi4iIigjRi0iJVNdKiRGLiIiKSNGLSImPy4lKiRGLiIiKiNGLSInISlHTyokRi4iIzUjRi0iKCspR09GJUYlRiU=

x:=1;

NiM+SSJ4RzYiIiIi

approx:=evalf(p(x));

NiM+SSdhcHByb3hHNiIkIissPUc9RiEiKg==

absfehler:=evalf(exp(1)-approx);

NiM+SSphYnNmZWhsZXJHNiIkIiNGISIq

relfehler:=evalf((exp(1)-approx)/exp(1));

NiM+SSpyZWxmZWhsZXJHNiIkIis4XHVLKiohIz0=

restglied:=evalf(restglied);

NiM+SSpyZXN0Z2xpZWRHNiIkIisqNHApNG8hIzw=

restglied:=evalf((exp(1)/(11)!)*(1-0)**11);

NiM+SSpyZXN0Z2xpZWRHNiIkIisqNHApNG8hIzw=

vergleich:=evalf((restglied-absfehler)/restglied);

NiM+SSp2ZXJnbGVpY2hHNiIkIit6ZztOZyEjNQ==

restart;

Ganzezahlen und ein Teil der Rationalen Zahlen, die genug fr\374h abbrechen, um sie genau darstellen zu k\366nnen.

Die Anzahl Bits die zur Darstellung einer Zahl zur Verf\374gung stehen.

mit Hilfe der Approximation von Funktionen

Max_Value=(2^15)-1Min_Value=(2^15)

Max_Value=(2^31)-1Min_Value=(2^31)

Max_Value=(2^63)-1 Min_Value=(2^63)

Max_Value=(2-(2^-23))*(2^127) Min_Value=(2^-149);

Max_Value=(2-(2^-52))*(2^1023) Min_Value=(2^-1047);

restart;

z1:=7919;

NiM+SSN6MUc2IiIlPno=

printf("\t\t\t7919 in binary: %20d", convert(z1,binary));

7919 in binary: 1111011101111

z2:=0.96875;

NiM+SSN6Mkc2IiQiJnZvKiEiJg==

printf("\t\t\t0.96875 in binary: %20.10f", convert(z2,binary));

0.96875 in binary: 0.1111100000

z3:=17389;

NiM+SSN6M0c2IiImKlE8

printf("\t\t\17389 in hexadezimal: %20s", convert(z3,hex));

17389 in hexadezimal: 43ED

z4:=[0,0,1,1,0,0,0,1,0,1,0,1,1,1,0,0,1,1];

NiM+SSN6NEc2Ijc0IiIhRiciIiJGKEYnRidGJ0YoRidGKEYnRihGKEYoRidGJ0YoRig=

z5:=convert(z4,base,2,10);

NiM+SSN6NUc2IjcoIiInIiIqIiImIiIiRioiIiM=

zahl:=0;

NiM+SSV6YWhsRzYiIiIh

for i from 1 to nops(z5) do zahl:=zahl+op(i,z5)*10**(i-1): end do:zahl;

NiMiJydmNiM=

z6:=[0,1,2,3,4,5,6,7,8,9,14,13,12,11,10];

NiM+SSN6Nkc2IjcxIiIhIiIiIiIjIiIkIiIlIiImIiInIiIoIiIpIiIqIiM5IiM4IiM3IiM2IiM1

z7:=convert(z6,base,16,10);

NiM+SSN6N0c2Ijc0IiIhIiIpIiIjIiIoRiciIiZGKUYnIiIlRilGKCIiKkYqIiIkRipGLkYqRio=

zahl:=0;

NiM+SSV6YWhsRzYiIiIh

for i from 1 to nops(z7) do zahl:=zahl+op(i,z7)*10**(i-1): end do:zahl;

NiMiMyFHMkRTIyl6dHQo

restart;grund_sequenz1:=convert([101,37,135,213,254],base,256,10);

NiM+SS9ncnVuZF9zZXF1ZW56MUc2IjcvIiImIiIjIiIiIiIoIiIqIiIhIiIlRixGJ0YtRitGLEYp

zahl1:=0:for i from 1 to nops(grund_sequenz1) do zahl1:=zahl1+op(i,grund_sequenz1)*10**(i-1): end do:zahl1;

NiMiLkRyNC9YNCI=

verwandelte_sequenz1:=convert(grund_sequenz1,base,10,256);

NiM+STV2ZXJ3YW5kZWx0ZV9zZXF1ZW56MUc2IjcnIiQsIiIjUCIkTiIiJDgjIiRhIw==

grund_sequenz2:=convert([178,169,120,128,214],base,256,10);

NiM+SS9ncnVuZF9zZXF1ZW56Mkc2IjcuIiIlIiImIiIoIiIjIiIqIiIkIiIpRilGKiIiIkYqRis=

zahl2:=0:for i from 1 to nops(grund_sequenz2) do zahl2:=zahl2+op(i,grund_sequenz2)*10**(i-1): end do:zahl2;

NiMiLWFGUnk3Iyo=

verwandelte_sequenz2:=convert(grund_sequenz2,base,10,256);

NiM+STV2ZXJ3YW5kZWx0ZV9zZXF1ZW56Mkc2IjcnIiR5IiIkcCIiJD8iIiRHIiIkOSM=

grund_sequenz3:=convert([229,70,216,193,245],base,256,10);

NiM+SS9ncnVuZF9zZXF1ZW56M0c2IjcvIiIkRiciIiIiIiUiIidGKCIiKkYoIiImRixGLCIiIUYo

zahl3:=0:for i from 1 to nops(grund_sequenz3) do zahl3:=zahl3+op(i,grund_sequenz3)*10**(i-1): end do:zahl3;

NiMiLkxUOz5iMCI=

verwandelte_sequenz3:=convert(grund_sequenz3,base,10,256);

NiM+STV2ZXJ3YW5kZWx0ZV9zZXF1ZW56M0c2IjcnIiRIIyIjcSIkOyMiJCQ+IiRYIw==

grund_sequenz4:=convert([42,251,221,106,199],base,256,10);

NiM+SS9ncnVuZF9zZXF1ZW56NEc2IjcuIiIlIiImRihGJyIiI0YnIiIiIiIqRiciIidGKCIiKQ==

zahl4:=0:for i from 1 to nops(grund_sequenz4) do zahl4:=zahl4+op(i,grund_sequenz4)*10**(i-1): end do:zahl4;

NiMiLWFYVSJcYyk=

verwandelte_sequenz4:=convert(grund_sequenz4,base,10,256);

NiM+STV2ZXJ3YW5kZWx0ZV9zZXF1ZW56NEc2IjcnIiNVIiReIyIkQCMiJDEiIiQqPg==

uebermittlung:=(zahl1,zahl2,zahl3,zahl4);

NiM+SS51ZWJlcm1pdHRsdW5nRzYiNiYiLkRyNC9YNCIiLWFGUnk3IyoiLkxUOz5iMCIiLWFYVSJcYyk=

restart;b:=2;exponent:=5; e_min=-15; e_max:=16; c:=15; mantisse:=10;

NiM+SSJiRzYiIiIjNiM+SSlleHBvbmVudEc2IiIiJg==NiMvSSZlX21pbkc2IiEjOg==NiM+SSZlX21heEc2IiIjOw==NiM+SSJjRzYiIiM6NiM+SSltYW50aXNzZUc2IiIjNQ==

Epsilon:=evalf(b^(-mantisse));

NiM+SShFcHNpbG9uRzYiJCIrK11pbCgqISM4

Precision:=evalf(b^(-(mantisse-1)));

NiM+SSpQcmVjaXNpb25HNiIkIisrXTdgPiEjNw==

kleinste_Zahl:=evalf((b^(-15))*(b^(-(mantisse-1))));

NiM+SS5rbGVpbnN0ZV9aYWhsRzYiJCIreVdZZ2YhIzw=

gr\366sste_Zahl:=b^e_max;

NiM+SS1ncnxhenNzdGVfWmFobEc2IiImT2In

vorzeichen:=0;

NiM+SSt2b3J6ZWljaGVuRzYiIiIh

expo2:=[0,1,0,1,0];

NiM+SSZleHBvMkc2IjcnIiIhIiIiRidGKEYn

expo101:=convert(expo2,base,2,10);

NiM+SShleHBvMTAxRzYiNyQiIiEiIiI=

expo10:=0:for i from 1 to nops(expo101) do expo10:=expo10+op(i,expo101)*10**(i-1): end do:expo10;

NiMiIzU=

expo10:=expo10-c;

NiM+SSdleHBvMTBHNiIhIiY=

mant2:=[0,0,0,0,0,1,0,0,1,0,1];

NiM+SSZtYW50Mkc2IjctIiIhRidGJ0YnRiciIiJGJ0YnRihGJ0Yo

mant10:=0:for i from 1 to nops(mant2) do mant10:=mant10+op(-i,mant2)*b**(1-i): end do:evalf(mant10);

NiMkIisrK0QiRyIhIio=

zahl:=evalf(mant10*(b^expo10));

NiM+SSV6YWhsRzYiJCIrXWkhUislISM2

vorzeichen:=[1];

NiM+SSt2b3J6ZWljaGVuRzYiNyMiIiI=

zahl101:=27.14*10**2;

NiM+SSh6YWhsMTAxRzYiJCInKzlGISIj

exponent10:=11;

NiM+SStleHBvbmVudDEwRzYiIiM2

zahl10:=[4,1,7,2];

NiM+SSd6YWhsMTBHNiI3JiIiJSIiIiIiKCIiIw==

zahl2:=convert(zahl10,base,10,2);

NiM+SSZ6YWhsMkc2IjcuIiIhIiIiRidGKEYoRidGJ0YoRidGKEYnRig=

mantisse:=seq([op(-i,zahl2)],i=2..nops(zahl2));

NiM+SSltYW50aXNzZUc2IjYtNyMiIiE3IyIiIkYnRilGJ0YnRilGKUYnRilGJw==

exponent101:=exponent10+c;

NiM+SSxleHBvbmVudDEwMUc2IiIjRQ==

exponent10:=[6,2];

NiM+SStleHBvbmVudDEwRzYiNyQiIiciIiM=

exponent1:=convert(exponent10,base,10,2);

NiM+SSpleHBvbmVudDFHNiI3JyIiISIiIkYnRihGKA==

exponent:=seq([op(-i,exponent1)],i=1..nops(exponent1));

NiM+SSlleHBvbmVudEc2IjYnNyMiIiJGJzcjIiIhRidGKQ==

computerdarstelleung:=(vorzeichen, exponent, mantisse);

NiM+STVjb21wdXRlcmRhcnN0ZWxsZXVuZ0c2IjYzNyMiIiJGJ0YnNyMiIiFGJ0YpRilGJ0YpRidGKUYpRidGJ0YpRidGKQ==