Sistema de numeracion

a) 10110 = 1 x 24 + 1 x 22 + 1 x 21 = 22
b) 10001101 = 1 x 27 + 1 x 23 + 1 x 22 + 1 x 20 = 141
c) 100100001001 = 1 x 211 + 1 x 28 + 1 x 23 + 1 x 20 = 2313
d) 1111010111 = 1 x 29 + 1 x 28 + 1 x 27 + 1 x 26 + 1 x 24 + 1 x 22 + 1 x 21 + 1 x 20 = 983
e) 10111111 = 1 x 27 + 1 x 25 + 1 x 24 + 1 x 23 + 1 x 22 + 1 x 21 + 1 x 20 = 191

A)
B)
37 | = | 2 | x | 18| + | 1 |
18 | = | 2 | x | 9 | + | 0 |
9 | = | 2 | x | 4 | + | 1 |
4 | = | 2 | x | 2 | + | 0 |
2 | = | 2 | x | 1 | + | 0 |
1 | = | 2 | x | 0 | + | 1 |
37 = 100101
C)
14 | = | 2 | x | 7 | + | 0 |
7 | = | 2 | x | 3 | + | 1 |
3 | = | 2 | x | 1 | + | 1 |
1 | = | 2 | x | 0 | + | 1 |
17 = 1110
D)
189 | = | 2 | x | 94 | + | 1 |
94 | = | 2 | x | 47 | + | 0 |
47 | = |2 | x | 23 | + | 1 |
23 | = | 2 | x | 11 | + | 1 |
11 | = | 2 | x | 5 | + | 1 |
5 | = | 2 | x | 2 | + | 1 |
2 | = | 2 | x | 1 | + | 0 |
1 | = | 2 | x | 0 | + | 1 |
189 = 0111101
E)
205 | = | 2 | x | 102 | + | 1 |
102 | = | 2 | x | 51 | + | 0 |
51 | = | 2 | x | 25 | + | 1 |
25 | = | 2 | x | 12 | + | 1 |
12 | = | 2 | x | 6 | + | 0 |
6 | = | 2 | x | 3 | + | 0 |
3 | =| 2 | x | 1 | + | 1 |
1 | = | 2 | x | 0 | + | 1 |
205 = 11001101
F)
2313 | = | 2 | x | 1156 | + | 1 |
1156 | = | 2 | x | 578 | + | 0 |
578 | = | 2 | x | 289 | + | 0 |
289 | = | 2 | x | 144 | + | 1 |
144 | = | 2 | x | 72 | + | 0 |
72 | = | 2 | x | 36 | + | 0 |
36 | = | 2 | x | 18 | + | 0 |
18 | = | 2 | x | 9 | + | 0 |
9 | = | 2 | x | 4 | + | 1 |
4 | = | 2 | x | 2 | + |0 |
2 | = | 2 | x | 1 | + | 0 |
1 | = | 2 | x | 0 | + | 1 |
2313 = 100100001001
G)
511 | = | 2 | x | 255 | + | 1 |
255 | = | 2 | x | 127 | + | 1 |
127 | = | 2 | x | 63 | + | 1 |
63 | = | 2 | x | 31 | + | 1 |
31 | = | 2 | x | 15 | + | 1 |
15 | = | 2 | x | 7 | + | 1 |
7 | = | 2 | x | 3 | + | 1 |
3 | = | 2 | x | 1 | + | 1 |
1 | = | 2 | x | 0 | + | 1 |
511 = 111111111EN 8 BITS EL NÚMERO MÁXIMO ES 255.
EN 16 BITS EL NÚMERO MÁXIMO ES 65534.

7438 = 7 x 82 + 4 x 81 + 3 x 80 = 483
368 = 3 x 81 + 6 x 80 = 30
37778 = 3 x 83 + 7 x 82 + 7 x 81 + 7 x 80 = 2047
2578 = 2 x 82 + 5 x 81 + 7 x 80 = 175
12048 = 1 x 83 + 2 x 82 + 4 x 80 = 644

A)
B) 598 = 73
59 | = | 8 | x | 7 | + | 3 |
7 | = | 8 | x | 0 | + | 7 |

C) 3728 = 566
372 | = | 8 | x| 46 | + | 6 |
46 | = | 8 | x | 5 | + | 6 |
5 | = | 8 | x | 0 | + | 5 |

D) 9198 = 1627
919 | = | 8 | x | 114 | + | 7 |
114 | = | 8 | x | 14 | + | 2 |
14 | = | 8 | x | 1 | + | 6 |
1 | = | 8 | x | 0 | + | 1 |

E) 65,5368 = 101.42233…
65 | = | 8 | x | 8 | + | 1 |
8 | = | 8 | x | 1 | + | 0 |
1 | = | 8 | x | 0 | + | 1 |

0.536 X 0.288 X 0.304 X 0.432 X0.456 X 0.648 X
8 8 8 8 8 8
4.288 2.304 2.432 3.456 3.648 5.184

0.184 X 0.472 X 0.776 X 0.432 X 0.208 X 0.664 X
8 8 8 8 8 8
1.472 3.776 2.432 6.208 1.664 5.312

0.312 X 0.496 X 0.968 X 0.744 X 0.952 X 0.616 X
8 8 8 8 8 8
2.496 3.9687.744 5.952 7.616 4.928

0.928 X 0.424 X 0.392 X 0.136 X 0.088 X 0.704 X
8 8 8 8 8 8
7.424 3.392 3.136 1.088 0.704 5.362

F) 2558 = 377
255 | = | 8 | x | 31 | + | 7 |
31 | = | 8 | x | 3 | + | 7 |
3 | = | 8 | x | 0 | + | 3 |

2.6.
3438 = 1111000112

483 | = | 2 | x | 241 | + | 1 |
241 | = | 2 | x |120 | + | 1 |
120 | = | 2 | x | 60 | + | 0 |
60 | = | 2 | x | 30 | + | 0 |
30 | = | 2 | x | 15 | + | 0 |
15 | = | 2 | x | 7 | + | 1 |
7 | = | 2 | x | 3 | + | 1 |
3 | = | 2 | x | 1 | + | 1 |
1 | = | 2 | x | 0 | + | 1 |
308 = 111102
30 | = | 2 | x | 15 | + | 0 |
15 | = | 2 | x | 7 | + | 1 |
7 | = | 2 | x | 3 | + | 1 |
3 | = | 2 | x | 1 | + | 1 |
1 | = | 2 | x | 0 | + | 1...