what is the mantissa and exponent values of 6.75 is represented in 8-but binary floating-point representation
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Answer:
Mantissa = 101 1000
Exponent = 1000 000
Explanation:
6(10) = 110(2)
multiplying = integer + fractional part;
0.75 × 2 = 1 + 0.5;
0.5 × 2 = 1 + 0
0.75(10) = 0.11(2)
Positive number before normalization:
6.75(10) = 110.11(2)
110.11(2) × 20 =
1.1011(2) × 22
Mantissa (not normalized): 1.1011
Exponent (unadjusted) + 2(8-1) - 1 =
2 + 2(8-1) - 1 =
(2 + 127)(10) =
129(10)
• division = quotient + remainder;
• 129 ÷ 2 = 64 + 1;
• 64 ÷ 2 = 32 + 0;
• 32 ÷ 2 = 16 + 0;
• 16 ÷ 2 = 8 + 0;
• 8 ÷ 2 = 4 + 0;
• 4 ÷ 2 = 2 + 0;
• 2 ÷ 2 = 1 + 0;
• 1 ÷ 2 = 0 + 1;
129(10) =1000 0001(2)
Exponent = 1000 0001
Mantissa =101 1000
6.75(10) = 0-10000001-1011000
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