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Enters! conversi a base b
em divisions sccessives i ens /edem amb
els restes.
Eemple! $ en base
$=11+111="+1
"=+1
=1+0
$=10111%
Fixeu-vos que s'escriu en el sentitinvers: el primer reste s la xifra de les
"unitats", el segon "desenes", ... i en la
divisi ltima el quocient s la primera
xifra.
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Representaci de reals en pnt
=dp
dp-1
...d1
d0
.d-1
d-
d-$
...(b
,amb 0di
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Reals en pnt ! conversi a base b
3a part entera %es/erra pnt decimal4 la
tractem com n enter5 la part *raccion6rias'obt7 *ent sccessis prodctes i /edant-seamb la part entera.
Eemple! $.1" en base $=10111%
0.1"=0.$ 0.=0.#
0.$=0.8 0.#=0.&
0.8=1. 0.&=1.8 0.8=1. 9.
0.1"=0.0010011001%
$.1"=10111.0010011001...%
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Representaci de reals en pnt :otant
=%-14s;%b
bE on s 0,1> 7s el si?ne,
E %eponent4 7s n enter,
; %mantissa4=d0.d
-1d
-d
-$... ,0d
i
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odicaci d'enters
(mb nbits es representen nvalors di*erents
Enters positis! entre 0i n-1! en base
Enters positis i ne?atis! complement a 2, entre -n-1i n-1-1
Clcul del complement a 2:
Ci el nombre 7s positi %0AAn-1-14 es representa en base amb nbits
Ci 7s ne?ati %-n-1A
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Eemple! complement a
n=1
000=1111101000%
-000
anvia 0 D 1
+1
011111010000
011111010000 100000101111
100000110000
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Eemple! -n-1
n=1
11=100000000000%
-11
anvia 0 D 1
+1
100000000000
100000000000 011111111111
100000000000
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Eemple n="
15 01111
14 0111013 01101
12 01100
11 01011
10 01010
9 010018 01000
7 00111
6 00110
5 00101
4 001003 00011
2 00010
1 00001
0 00000
15 01111
14 0111013 01101
12 01100
11 01011
10 01010
9 010018 01000
7 00111
6 00110
5 00101
4 00100
3 00011
2 00010
1 00001
0 00000
-1 11111
-2 11110-3 11101
-4 11100
-5 11011
-6 11010
-7 11001-8 11000
-9 10111
-10 10110
-11 10101
-12 10100-13 10011
-14 10010
-15 10001
-16 10000
-1 11111
-2 11110-3 11101
-4 11100
-5 11011
-6 11010
-7 11001-8 11000
-9 10111
-10 10110
-11 10101
-12 10100
-13 10011
-14 10010
-15 10001
-16 10000
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Cmes en complement a
5+1 = ?5 00101
1 00001
6 00110
5+1 = ?5 00101
1 00001
6 00110
14-7 = ?
14 01110
-7 11001
7 100111
14-7 = ?
14 01110
-7 11001
7 100111
Aritmtica a/(2n)Aritmtica a/(2n)
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odicaci de reals en pnt :otant
=%-14s;%b
bE on s 0,1> 7s el si?ne,
E 7s n enter, ;=F0.F
1F
F
$... ,0F
i
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3'est6ndard JEEE 2"#
Es treballa en base , per tant d0@0 implica d
0=1
%no es ?arda4, m= 1.d1d
...d
p=1.*
Krecisi simple (float4 es ?arda en $ bits
1 bit! si?ne %s4 L0 per positiM
& bits! E+12 %e, ep modicat4 L12=8-1-1, biaixM
$ bits! $ bits de *racci %f4
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3'est6ndard JEEE 2"#
Krecisi doble %double4 es ?arda en 8# bits
1 bit! si?ne %s4 L0 per positiM
11 bits! E+10$ %e4 L10$=11-1
-1, biaixM" bits! " bits de *racci %f4
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alors JEEE 2"# %precisi simple4
e="" * @ 0, NaN%Not a Nmber4
e="" * = 0, (-1)s
0
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alors JEEE 2"# %precisi doble4
e=0#2 * @ 0, NaN%Not a Nmber4
e=0#2 * = 0, (-1)s
0
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=10. en precisi simple
O=10.=".1 1=."" =1.2" &
%posem 1!% '2, o P les ve?ades necess6ries 4
1.2"=1.010 0011 0011 0011 00119.
E=&, e=&+12=1$0 = 10000010%
s=0 %positi4
01000001001000110011001100110011
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Qin valor 7s exactament
01000001001000110011001100110011
10000010%=1&0, E=1&0-12=$
s=0 %positi4
m=1.01000110011001100110011%
1+-2+-$+-#+-10+-11+-1+-1*+-18+-1++-22+-2&=
1+%21+1#+1$+1&+12+++8+*++1+14P2& =
1+$08&82P&$&&80& =
1!2#++++#$1*81208+8*00!!!!
,("2&) ,10!1+++++80+2$*1&$#18#*0000000!!!
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Qin valor el se?ei
(1!2#++++#$1*81208+8*00!!!! .2-2&) "2&
01000001001000110011001100110100
10000010%=1&0, E=1&0-12=$
s=0 %positi4
m=1.01000110011001100110100%
1+-2+-$+-#+-10+-11+-1+-1*+-18+-1++-21=
1+%21+1#+1$+1&+12+++8+*++4P2& =
1+$08&8&P&$&&80& ,1!2#*0000+*&$#&1$0$2*0000000!!!! ("2&) ,
10!200000#$2+&+*&12*000000!!!
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=-0.1 en precisi simple
=-0.1=-0. -1=-0.# -=-0.& -$=-1.8 -
1.8=1.1001 1001 1001 1001 1001 10019.
E=-, e=-+12=1$ = 01111011%
s=1 %ne?ati4
10111101110011001100110011001101
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Qin valor 7s exactament
10111101110011001100110011001101
011110110%=12&, E=12&-12=-#
s=1 %ne?ati4
m=1.10011001100110011001101%
1+-1+-+-*+-8+-++-12+-1&+-1$+-1#+-20+-21 +-2&
, 1+"0$$18"P&$&&80&
,1!$0000002&818*#+101*$2*000000!!!!
-("2-) ,-0!100000001+011$11+&8#$*$2*000!!!
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Qin valor el se?ei
-(1!$0000002&818*#+101*$2*000!! -2-2&) /2-
10111101110011001100110011001100
011110110%=12&, E=12&-12=-#
s=1 %ne?ati4
m=1.10011001100110011001100%
1+-1+-+-*+-8+-++-12+-1&+-1$+-1#+-20+-21 ,
1+"0$$18#P&$&&80& =
1! *++++++0$&2*$8&*+*0000!!!!
-("2-) ,-0!0+++++++0&+*&**22$0+*000!!!
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Els nombres :otantsS en la recta real
Copyright Journal of Artificial Societies and Social Simulation, [2006]
http://jasss.soc.surrey.ac.uk/admin/copyright.htmlhttp://jasss.soc.surrey.ac.uk/admin/copyright.html
