Respostas Lista 6 Copia

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SEL0414 - Sistemas Digitais
Resoluc¸a˜o Lista 6 - Sistemas de Numerac¸a˜o
01
a.
(10110)b = 2
4 + 22 + 21 = 21
b.
(1001000001001)b = 2
12 + 29 + 23 + 20 = 4617
c.
(11111111)b = 2
7 + 26 + 25 + 24 + 23 + 22 + 21 + 20 = 28 − 1 = 255
d.
(100110)b = 2
5 + 22 + 21 = 38
e.
(1111010111)b = 2
9 + 28 + 27 + 26 + 24 + 22 + 21 + 20 = 983
02
a.
37 = 2 · 18 + 1 = 22 · 9 + 1 = 22 · (2 · 4 + 1) + 1 = 25 + 22 + 20 = (100101)b
b.
189 = 2 · 94 + 1 = 22 · 47 + 1 = 22 · (2 · 23 + 1) + 1 = 23 · 23 + 22 + 1 = 23 · (11 · 2 + 1) + 22 + 1 =
24 ·11+23+22+1 = 24 ·(2 ·5+1)+23+22+1 = 25 ·5+24+23+22+1 = 25 ·(2 ·2+1)+24+23+22+1 =
27 + 25 + 24 + 23 + 22 + 20 = (10111101)b
c.
77 = 2 ·38+1 = 22 ·19+1 = 22 ·(2 ·9+1)+1 = 23 ·9+22+1 = 23 ·(2 ·4+1)+22+1 = 26+23+22+20 =
(1001101)b
d.
205 = 2 · 102 + 1 = 22 · 51 + 1 = 22 · (2 · 25 + 1) + 1 = 23 · 25 + 22 + 1 = 23 · (2 · 12 + 1) + 22 + 1 =
24 · 12 + 23 + 22 + 1 = 25 · 6 + 23 + 22 + 1 = 26 · 3 + 23 + 22 + 1 = 27 + 26 + 23 + 22 + 20 = (11001101)b
e.
511 = 512 − 1 = 29 − 1 = 28 + 27 + 26 + 25 + 24 + 23 + 22 + 21 + 20 = (11111111)b
1
03
a.
(B0B0)h = 11 · 163 + 11 · 161 = 45232
b.
(37FD)h = 3 · 163 + 7 · 162 + 15 · 161 + 13 = 14333
c.
(FE10)h = 15 · 163 + 14 · 162 + 1 · 161 = 65040
d.
(7FF )h = 7 · 162 + 15 · 161 + 15 = 2047
04
a.
59 = 3 · 16 + 11 = (3B)h
b.
919 = 57 · 16 + 7 = (3 · 16 + 9) · 16 + 7 = 3 · 162 + 9 · 16 + 7 = (397)h
c.
771 = 48 · 16 + 3 = 3 · 162 + 3 = (303)h
05
a.
(5432)h = (0101 0100 0011 0010)b
b.
(1322)h = (0001 0011 0010 0010)b
c.
(2435)h = (0010 0100 0011 0101)b
d.
(2110)h = (0010 0001 0001 0000)b
2
07
a.
(5432)8 = 5 · 83 + 4 · 82 + 3 · 81 + 2 · 80 = 2842
b.
(1322)4 = 1 · 43 + 3 · 42 + 2 · 41 + 2 · 40 = 122
c.
(2435)5 = 2 · 53 + 4 · 52 + 3 · 51 + 5 · 50 = 370
d.
(2110)3 = 2 · 33 + 1 · 32 + 1 · 31 + 0 · 30 = 66
08
a.
47 = (0100 0111)BCD
b.
187 = (0001 1000 0111)BCD
c.
13 = (0001 0011)BCD
d.
89627 = (1000 1001 0110 0010 0111)BCD
e.
72 = (0111 0010)BCD
3