You may work with your classmates on these problems. If you work closely with another person,
feel free to submit your work jointly. Please, don't submit work from more than two people.
Submit as PDF via Moodle.
- (P&H 5th edition, problem 3.22) What decimal number does the bit pattern 0x0C000000 represent
if it is an IEEE 754 single precision floating point number?
- (Problem 3.23) Write down the binary representation of the decimal number
63.25 assuming the IEEE 754 single precision format. (Give your final answer
as an 8-digit hexadecimal number.)
- (Problem 3.24) Write down the binary representation of the decimal number
63.25 assuming the IEEE 754 double precision format. (Give your final answer
as a 16-digit hexadecimal number.)
- Write down the binary representation of the decimal number
3.7 assuming the IEEE 754 single precision format. (Give your final answer
as an 8-digit hexadecimal number.)
- The following questions concern IEEE 754
32-bit floating point numbers. When I refer to a "representable
number," I mean a number whose exact value is one of the values
that has a 32-bit IEEE 754 representation.
- What is the smallest positive integer that is not representable?
- What is the largest representable positive integer?
- What is the smallest positive normalized number?
- What is the largest positive denormalized number?
- In one of the textbook's earlier editions, there is a paragraph describing
a pre-IEEE 754 floating point processor that lacked a guard bit. The paragraph
describes a common trick used by programmers that involved writing
"(0.5 - x) + 0.5" instead of "1.0 - x" in FORTRAN or C programs
to "compensate for the lack of a guard digit." Explain in detail why the lack of a guard digit
makes the sensible "1.0 - x" fail while "(0.5 - x) + 0.5" succeeds.
- Suppose I store a letter to my sister in an ASCII file called letter.txt, and the letter
begins "Dear Jody". Now suppose I write a C program that (1) opens letter.txt, (2) reads
the first four bytes into an int variable k, and (3) prints k as a decimal number (via
the statement printf("%d\n", k)).
If I am using a computer with an Intel Pentium processor (little-endian), what output does this
program produce? If I am using a computer with a Motorola 68060 processor (big-endian), what output
does the program produce? (These chip examples require you to travel back to 1993 when Java was
young and games on CD-ROM were the hot new thing. These days, most processors are either little endian
or configurable to go either way ("bi-endian").)