Number Representations on Digital Computers

Numeral Systems

1. Define the following terms:
   • numeral system
   • positional notation
   • decimal numeral system
   • binary numeral system

2. Explain and use the decimal numeral system to represent an integer.

3. Explain and use the binary numeral system to represent an integer.

4. Convert the binary representation of an integer to the decimal representation and vice versa.

Binary Representations of Real Numbers

1. Explain and use the decimal numeral system to represent a non-repeating decimal fraction.

2. Explain and use the binary numeral system to represent a non-repeating binary fraction.

3. Give examples of repeating binary fractions and explain why they cannot be represented on a computer with finite memory.

Floating Point Numbers

1. Define the following terms:
   • floating point number
   • mantissa

2. Explaining why the floating point representation of a number is so-named.

3. State the standard Python uses for floating point numbers.

4. Give the performance characteristics of a double-precision floating-point number.

Printing Floating Point Numbers in Python

1. Use the % operator to print a floating point number to a desired number of decimal places.