Représentation des nombres en machine

IN
N=xn0×2n0+· · · +xk×2k+· · · +x1×2 + x0
n0
x0xn0
→
IN
IN= (xn0· · · x1x0)2
→271 = 256 + 8 + 4 + 2 + 1
= 1 ×28+ 0 ×27+ 0 ×26+ 0 ×25+ 0 ×24
+1 ×23+ 1 ×22+ 1 ×21+ 1 ×20
271 = 1 0000 11112
→1100102
0×20+ 1 ×21+ 0 ×22+ 0 ×23+ 1 ×24+ 1 ×25= 50
255 65 535
N
:::::::::::::::::::::::::::::::::::
28= 256
28−1
−2727−1
:::::::::::::::::::::::::
 n 27−1
 n −27−1
28+n28−27= 2728−1
1111 11112

I
11,01012= 1 ×21+ 1 ×20+ 0 ×2−1+ 1 ×2−2+ 0 ×2−3+ 1 ×2−4
= 2+1+0+0,25 + 0 + 0,0625
= 3,3125
Ix
x=s m 2n
s x
m[1,2[
n
x= 3,3125 x= +1,65625 ×21
1,65625
x
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
•+−
•n
n+ 1023
•m[1,2[
s m 2ns m ∈[1,2[ n∈Z
→
∞
→
→
::::::::::::::::::::::::::::::::::::::::::
0,4 0,011001100110011 · · ·2
0,4
0,400000000000000022204460492503