Question

what is the mantissa and exponent values of 6.75 is represented in 8-but binary floating-point representation

Answer 1

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