Solução dos Exercícios Ponto Flutuante

1a) 158,125d = 10011110,001b = 1.0011110001 x 2^7

 Sinal = 0b
 Expoente = 7 + 127 = 134 = 10000110b
 Mantissa = (1,)0011110001b = 00111100010000000000000

Portanto:

 158,125d = 01000011000111100010000000000000b

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1b) 490,5625d = 111101010,1001b = 1,111010101001b x 2^8

 Sinal = 0
 Expoente = 8 + 127 = 135 = 10000111b
 Mantissa = (1,)111010101001b = 11101010100100000000000

Portanto:

  490,5625d = 01000011111101010100100000000000b

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2a) 1110.0001.0110.0000.0000.0000.0000.0000b

 = 1 11000010 (1,)11000000000000000000000b

Sinal: - Expoente: 11000010b = 194d ⇒ 194 - 127 = 67 Mantissa: 1,1100 = 1,75d

⇒ 1,75 . 2^67 = 1,75 . 147573952589676412928 = 258254417031933722624d
 

Portanto:

 1110.0001.0110.0000.0000.0000.0000.0000b = -2,75. 2^67 d = -258.254.417.031.933.722.624d

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2b) 0010.1000.1001.0101.0000.0000.0000.0000b

  = 0 01010001 (1,)00101010000000000000000

Sinal: + Expoente: 01010001 = 81 ⇒ 81 - 127 = -46 Mantissa: 1,0010101 = 1,1640625

 ⇒ 1,1640625 . 2^-46 = 1,1640625 . 1,4210854715202003717422485351563e-14 = 1,6542323066914832452312111854553e-14

Portanto:

 0010.1000.1001.0101.0000.0000.0000.0000b = 1,6542323066914832452312111854553e-14