Question

Circle the correct answer or write the correct answer in the space provided.

1. Quoting our text book, “A fraction with a nonzero leftmost digit is said to be normalized.” For example, 10.011₂ ´ 2^-3 is normalized by shifting the binary point 2 places to the left and increasing the exponent by 2 yielding 0.10011₂ ´ 2^-1. The mantissa, m, of every correctly normalized non-zero floating-point number, ± m ´ 2^exponent, satisfies the relationship m Î

A: [ 0.0,1.0 ] B: [ 0.1,1.0 ] C: ( 0.1,1.0 ) D: [ 0.1,1.0 ) E: ( 0.1,1.0 ]

2. T or F? Floating-point computations always yield exact answers except when underflow or overflow occurs.

3. T or F? Floating-point underflow and overflow occur because the mantissa field’s lack of precision.

4. T or F? Every 32-bit combination of the IEEE Standard 754 single-precision floating-point number is a real number that can be found on the real number line.

5. Which aspect of the floating point representation is doubled going from IEEE Standard 754 single-precision to double-precision?
A: exponent size B: mantissa precision C: mantissa range D: exponent range E: none of these

6. T or F? Because of its “double-ness” double-precision floating-point addition usually produces an exact answer, not merely an approximate answer.

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 ´ 2^exponent where

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

Answer 1