國立暨南國際大學 108 學年度第一學期期中考試卷

1. (10%) Convert the following hexadecimal numbers into decimal (assuming unsigned integers).
• 56
• FF
• B5
• 5A
• FE
  
  
2. (10%) Add the following octal numbers.  The answer should be written as an octal number.
   
• 126
• 377
• 265
• 132
• 376
  
  
3. (10%) Answer the following questions.
   1. When we say the size of a variable is "4 bytes", that is equivalent to how many bits?
   2. If the variable is used to store a signed integer, what is the largest and smallest integer it can store, respectively? (You may write a mathematical formula for calculating the numbers.)
   3. If the variable is used to store an unsigned integer, what is the largest and smallest integer it can store, respectively? (You may use a mathematical formula for calculating the numbers.)
      
      
4. (10%) Determine whether the syntax of the following code is correct or not.  If it is correct, predict its output.  If it is incorrect, point out the mistake(s).
   // Condition
   #include <iostream>
   using std::cout;
   
   int main()
   {
       int n = 100;
       int sum = 0;
       while (n > 0)
       {
           sum += n;
           if (n = 0)
               break;
           --n;
       }
       cout << n << ' ' << sum << '\n';
       return 0;
   }
   
   
5. (10%) What will the following code display?
   
   // Two's Complement
   #include <iostream>
   using std::cout;
   using std::endl;
   
   int main()
   {
       signed short n = 1;
       n = n << 15; cout << n << '\t';
       n = n >> 1; cout << n << '\t';
       n = n ^ -1; cout << n << '\t';
       n = n >> 4; cout << n << '\t';
       n = n + 32513; cout << n << '\n';
       return 0;
   }


6. (10%) What will the following code display?
   
   // Bitwise Shift
   #include <iostream>
   using std::cout;
   
   int main()
   {
       short n = 10;
       n <<= 1; cout << n << '\t';
       n <<= 2; cout << n << '\t';
       n <<= 4; cout << n << '\t';
       n >>= 3; cout << n << '\t';
       n /=  8; cout << n << '\n';
       return 0;
   }
   
   
7. (10%) Determine whether the syntax of the following code is correct or not.  If it is correct, predict its output.  If it is incorrect, point out the mistake(s).
   //  Nested for-loop
   #include <iostream>
   using std::cout;
   using std::endl;
   
   int main()
   {
       int i=1, j=1;
       int sum=0;
       for ( ; i<=9; i++)
           for ( ; j<=9; j++)
               sum += (i*10+j);
       cout << sum << endl;
       return 0;
   }
   
   
8. (10%) What will the following code display?
   
   // De Morgan's Law
   // std::boolalpha
   #include <iostream>
   using std::cout;
   using std::boolalpha;
   
   int main()
   {
       int p, q;
       cout << "P\tQ\t~(P&&Q)\t~P||~Q\n";
       cout << boolalpha;
       for (p=0; p<=1; p++)
           for (q=0; q<=1; q++)
               cout << static_cast<bool>(p) << '\t'
                    << static_cast<bool>(q) << '\t'
                    << !(p&&q) << '\t'
                    << (!p || !q) << '\n';
       return 0;
   }
   
   
9. (10%) What will the following code display?
   
   // Euclidean algorithm for GCD
   #include <iostream>
   using std::cout;
   using std::endl;
   
   int main()
   {
       int a=54, b=72;
       int temp;
       while (b!=0)
       {
           a %= b;
           temp = a; a = b; b = temp;
       }
       cout << a << '\t' << b << endl;
       return 0;
   }
   
   
10. (10%) What will the following code display?
    
    // while-loop
    #include <iostream>
    using std::cout;
    
    int main()
    {
        bool first = true;
        const int n = 7*25*27;
        for (int m=n, i=3; m>1; i+=2)
            while (m / i * i == m)
            {
                if (first)
                    first = false;
                else
                    cout << '*';
                cout << i;
                m /= i;
            }
        cout << '\n';
        return 0;
    }
    
    
11. (10%) What will the following code display?
    
    // Syracuse Sequence
    #include <iostream>
    using std::cout;
    using std::endl;
    
    int main()
    {
        int n = 3;
        while (n > 1)
        {
            cout << n << ' ';
            if (n % 2)
                n = 3 * n - 1;
            else
                n = n / 2;
        }
        cout << n << endl;
        return 0;
    }