7. T or F? All positive IEEE Standard 754 denormalized numbers are strictly less

Question

7. T or F? All positive IEEE Standard 754 denormalized numbers are strictly less than the smallest positive normalized number.

8. ____________________ Use n to write an expression which computes the excess amount for the n-bit excess notation used by the IEEE Standard 754. Hint When n = 8 (single precision), the excess amount is 127; when n = 11 (double precision), the excess amount is 1023.

9. T or F? Increasing the number of bits in the IEEE Standard 754 significand improves the precision or accuracy of the real number approximation.

10. ____________________ Convert the IEEE 754 single-precision floating-point number BF69800016 to decimal.

11. ________________________________________ Convert 93/128 to IEEE 754 double-precision format. Express your answer as sixteen hexadecimal nibbles.

12. ____________________ Convert the IEEE 754 single-precision floating-point number 8000000F16 to binary expressed in normalized scientific notation. Hint 8000000F16 is a denormalized number.

13. ____________________ Convert the IEEE 754 double-precision floating-point number FFF123456789ABCD16 to binary expressed in normalized scientific notation.

14. ____________________ What is the excess-1023 exponent value of the IEEE 754 double-precision floating-point number

x = D1BFED012345678916 expressed in decimal; that is, the value of the exponent field found in the 64-bit representation?

15. ____________________ (Continuing 14) What is the exponent of the double-precision number x expressed in decimal; that is, the value of exponent when the floating-point number x is expressed using the notation ± significand ´ 2exponent where

significand Î [ 1.00...02,1.11...12 ]?

Explanation / Answer

9. True

Because in binary single precision floationg point is s=1.10010010000111111011011 and here e=1.For this the decimal value is 3.1415927410125732421875 , for more accuracy the approximation of the true value is 3.14159265358979323846264338327950...

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