c_numeration.pdf

Systmes de numration : exercices http://electroussafi.ueuo.com/ N. ROUSSAFI

Systmes de numration

corrig

Exercice 1

1) (101011101)2 = 1x28 + 0x27 + 1x 26 + 0x25 + 1x24 + 1x23 + 1x22 + 0x21 + 1x20

(101011101)2 = 256 + 0 + 64 + 0 + 16 + 8 + 4 + 0 + 1 = (349)10

%1110001 = (1110001)2 = 1110001B = (113)10

101101,1001B = 1x25 + 0x24 + 1x 23 + 1x22 + 0x21 + 1x20 + 1x2-1 + 0x2-2 + 0x2-3 + 1x2-4

101101,1001B = (45,5625)10

2) (745)8 = 7x82 + 4x81 + 5x80 = 7x64 + 4x8 + 5 = (485)10

(123)8 = (83)10

(2454,46)8 = 2x83 + 4x82 + 5x81 + 4x80 + 4x8-1 + 6x8-2 = (1324,59375)10

3) (A9C)16 = 10x162 + 9x16 +12 = 2716 $F23 = F23H = (F23)16 = (3875)10

12,5H = 1x161 + 2 x160 + 5x16-1 = (18,3125)10

Exercice 2

1)

(54)10 = ( ? )2 54 2 0 27 2 1 13 2 1 6 2

Sens de lecture

0 3 2 1 1 2 1 0

(54)10 = (110110)2 (83)10 = (1010011)2 (15,6)10 = (15)10 + (0,6)10 (15)10 = (1111)2 (0,6)10 = ( ? )2


0,6 x 2 = 1,2 = 1 + 0,2

0,2 x 2 = 0,4 = 0 + 0,4 Sens de (0,6)10 = (0,1001)2

0,4 x 2 = 0,8 = 0 + 0,8 lecture

0,8 x 2 = 1,6 = 1 + 0,6

(15,6)10 = (1111)2 + (0,1001)2 =(1111,1001)2 2) (564)10 = ( ? )8

564 8 4 70 8 6 8 8 0 1 8 1 0

(564)10 = (1064)8 (83)10 = (123)8

(15,6)10 = ( ? )8 = (15)10 + (0,6)10 (15)10 = (17)8 0,6 x 8 = 4,8 = 4 + 0,8

0,8 x 8 = 6,4 = 6 + 0,4 (0,6)10 = (0,4631)8

0,4 x 8 = 3,2 = 3 + 0,2

0,2 x 8 = 1,6 = 1 + 0,6

(15,6)10 = (15)10 + (0,6)10 = (17)8 + (0,4631)8 = (17,4631)8

3) (1564)10 = ( ? )16

1564 16 12 (C) 97 16

1 6 16 6 0

(1564)10 = (61C)16 (83)10 = (53)16 (15,6)10 = ( ? )16 (15)10 = (F)16 (0,6)10 = ( ? )16 0,6 x 16 = 9,6 = 9 + 0,6

0,6 x 16 = 9,6 = 9 + 0,6 (0,6)10 = (0,999)16

0,6 x 16 = 9,6 = 9 + 0,6

(15,6)10 = ( ? )16 = (15)10 + (0,6)10 = (F)16 + (0,999)16 = (F,999)16


Exercice 3

Binaire hexadcimal 0 1 2 3 4 5 6 7 8 9 A B C D E F

0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111

Binaire octal

0 1 2 3 4 5 6 7 000 001 010 011 100 101 110 111

1) AC9H = (101011001001)2 $BD3 = (101111010011)2 (125)16 = (100100101)2 2) (1000110011)2 = (233)16 (10011110101)2 = (4F5)16 3) (754)8 = (111101100)2 (156)8 = (1101110)2 (10011110101)2= (2365)8 4) F65H = (111101100101)2 = (7545)8 (456)8 = (100101110)2 = (12E)16 (AC3)16 = (101011000011)2 = (5303)8

c_numeration.pdf

Documents