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<h3>Exercises</h3>
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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
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<pre>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</pre>
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<p>
Bitwise complement is denoted by a tilde ~. For instance (on a four-bit computer), if <i>k</i> = 13 (binary 1101) than its complement <i>j</i> = ~<i>k</i> would be equal to 2 (binary 0010) (ones become zeros and zeros become ones).
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<td colspan=2><b>Binary Bitwise Operators</b>
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<td>& <td>bitwise and
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<td>| <td>bitwise (inclusive) or
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<td>^ <td>bitwise exclusive or (xor)
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<td>>> <td>right shift by n bits
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<td><< <td>left shift by n bits
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<td colspan=2><b>Unary Bitwise Operator</b>
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<td>~ <td>one's complement
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<li>Add bitwise operations to our calculator.
<li>Add a new command, 'x', that toggles between decimal and hexadecimal outputs.
<p>To output a number in the hexadecimal (base sixteen) one sends a modifier "hex" to the output.
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<pre>using std::hex;
int i = 11;
cout << hex << i; // i will be printed in hex as 'b'.</pre>
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<li>Extend the calculator by adding <i>symbolic variables</i> 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
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<pre>> a
> 5
> = // a = 5
> 2
> a
> * // 2 * 5</pre>
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<p>
Consider what should the <var>Calculator</var> do with a symbol. For instance, what should it push on the stack?
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