### 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.