# 1.18. Programming Exercises

- Implement the simple methods
`getNum`

and `getDen`

that will
return the numerator and denominator of a fraction.
- In many ways it would be better if all fractions were maintained in
lowest terms right from the start. Modify the constructor for the
`Fraction`

class so that `GCD`

is used to reduce fractions
immediately. Notice that this means the `+`

function no
longer needs to reduce. Make the necessary modifications.
- Implement the remaining simple arithmetic operators (
`-`

,
`*`

, and `/`

).
- Implement the remaining relational operators (
`>`

,
`>=`

, `<`

, `<=`

, and `!=`

)
- Modify the constructor for the fraction class so that it checks to
make sure that the numerator and denominator are both integers. If
either is not an integer the constructor should raise an exception.
- In the definition of fractions we assumed that negative fractions
have a negative numerator and a positive denominator. Using a
negative denominator would cause some of the relational operators to
give incorrect results. In general, this is an unnecessary
constraint. Modify the constructor to allow the user to pass a
negative denominator so that all of the operators continue to work
properly.
- Repeat the last question but this time consider the
`+=`

method.
- Research other types of gates that exist (such as NAND, NOR, and
XOR). Add them to the circuit hierarchy. How much additional coding
did you need to do?
- The most simple arithmetic circuit is known as the half-adder.
Research the simple half-adder circuit. Implement this circuit.
- Now extend that circuit and implement an 8 bit full-adder.
- The circuit simulation shown in this chapter works in a backward
direction. In other words, given a circuit, the output is produced by
working back through the input values, which in turn cause other
outputs to be queried. This continues until external input lines are
found, at which point the user is asked for values. Modify the
implementation so that the action is in the forward direction; upon
receiving inputs the circuit produces an output.
- Design a class to represent a playing card. Now design a class to
represent a deck of cards. Using these two classes, implement a
favorite card game.
- Find a Sudoku puzzle in the local newspaper. Write a program to solve
the puzzle.

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