Exercises

In C++ one can perform bitwise operations on integral numbers. Binary bitwise operators AND and OR are denoted by ampersand & and vertical bar | respectively. The usage is

int i = 3; // binary 0011 int j = 5; // binary 0101 int k = i & j; // binary 0001 k = i | j; // binary 0111 k = k | 8; // binary 1111

Bitwise complement is denoted by a tilde ~. For instance (on a four-bit computer), if k = 13 (binary 1101) than its complement j = ~k would be equal to 2 (binary 0010) (ones become zeros and zeros become ones).

Binary Bitwise Operators
&	bitwise and
|	bitwise (inclusive) or
^	bitwise exclusive or (xor)
>>	right shift by n bits
<<	left shift by n bits
Unary Bitwise Operator
~	one's complement

1. Add bitwise operations to our calculator.
2. Add a new command, 'x', that toggles between decimal and hexadecimal outputs.

   To output a number in the hexadecimal (base sixteen) one sends a modifier "hex" to the output.

   using std::hex; int i = 11; cout << hex << i; // i will be printed in hex as 'b'.

3. Create a "logical calculator" that operates on Boolean values. Instead of numbers, it accepts t and f for true and false. It performs logical and, or, and not, and accepts &, |, and ! as tokens (notice the not is a unary operation--it takes one argument). Send the manipulator std::boolalpha to the output stream before printing Boolean values.
4. Extend the calculator by adding symbolic variables denoted by lowercase letters. Add the assignment operation that assigns a value to a symbolic variable. For instance, one should be able to do the following

   > a > 5 > = // a = 5 > 2 > a > * // 2 * 5

   Consider what should the Calculator do with a symbol. For instance, what should it push on the stack?