CMPSCI 145

Homework 3 Form
(Floating-Point)

CMPSCI 145 Students, Current Semester, Only!

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Smith, Fred Q.


HOMEWORK #3

Answer the following questions about floating-point binary numbers in various formats, both standard and non-standard (quarter-precision, half-precision, single-precision, and double-precision).



1. What is the true binary value of -69.8125?
2. What is the binary scientific value of the answer in part 1 (in ±x.xxxx*2^yyyy format)?
3. Yes or No: Can the number in part 2 be represented perfectly in quarter precision?
4. Yes or No: Can the number in part 2 be represented perfectly in half precision?
5. Yes or No: Can the number in part 2 be represented perfectly in single precision?
6. Yes or No: Can the number in part 2 be represented perfectly in double precision?
7. In decimal, what is the value of the biased exponent from the number in part 2 for single precision?
8. In binary, what is the value of the biased exponent from the number in part 2 for single precision?
9. What is the complete 32-bit binary representation for the number in part 2 in single precision?
10.In decimal, what is the value of the biased exponent from the number in part 2 for double precision?
11.In binary, what is the value of the biased exponent from the number in part 2 for double precision?
12.What is the complete 64-bit binary representation for the number in part 2 in double precision?
13.What is the value for infinity in quarter precision?
14.What is the value for infinity in half precision?
15.What is the value for infinity in single precision?