Correct Homework assigned 9/4, due 9/11
from "Numerical Mathematics and Computing"
pick up your xerox copy from outside 4C5
Changing Bases
1. Write 23.58 in base 8.
2. Write (81.33)_8 in base 10.
A very simple machine's number
Assume we have only 5 bits to represent a number and we're working in
base 3. The bits are divided as follows: one bit for the sign of the
number, two bits for the mantissa, and two bits for the exponent (one
for the exponent's sign and one for the exponent's value).
Specifically, the numbers are of the form:
+/- 0.b1 b2 3^{+/- m}
where b1,b2, and m are in {0,1,2}.
1. List all the machine numbers in this representation. List them
in base 10, either decimal notation 0.333333333 or as fractions,
1/3.
2. List three real numbers which are not machine numbers. What are
the absolute errors and the relative errors made in converting
them to machine numbers?
Section 2.2
Written problems: 1, 2, 7, 29, 30.
Computer problems: 1.
Section 2.3
1. Prove the upper bound of "theorem on loss of precision". (The
part of the proof that is left to the reader.)
Written problems: 1, 6, 9, 19, 23.
Computing problems: 5, 6, 14.