CSC231 Mystery C Program with signed numbers

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Mystery Program

• The program below is incomplete.
• The two values that were used to initialize x and y have been removed.
• We do have the output of the program, though, corresponding to the original x and y values.

Question 1

Figure out the value of x and y in the original program.

Question 2

Find a way to fix the program so that it outputs the correct information

You may use this converter to help you out...

/* mystery.cpp
// D. T.
// mystery program
// To compile and run this program:
//
//     g++ mystery.cpp
//     a.out
//
// The output of the program is the following
//
// 32740
// -32756
//
// With what positive values were x and y initialized
// at the beginning of the program.  Explain why.
// (a short int contains 16 bits)
*/

#include <stdio.h>

int main() {

    short int x = ???? ;
    short int y = ???? ;

    x = x+y;
    printf( "%d\n", x );

    x = x+y;
    printf( "%d\n", x );

    return 0;
}

For reference, 2¹⁵ = 32768.

Solution

Answer 1

• First we need to find the unsigned version of -32756, because that is the value we expected, but this value is too large to be represented in 2's complement.
• The difference between a negative 16-bit number in 2's complement, and its unsigned equivalent is 2¹⁶, of 65536.
• So, -32756 which is printed, has an unsigned value of -32756 + 65536 = 32780.
• So, x+y is 32740 and x+y+y = 32780
• Therefore y = 40
• Therefore x = 32700
• Plug these numbers in the program and verify that we get, indeed, the two numbers listed in the comment section of the program.

Answer 2

• We could switch from shorts to ints
• We could use unsigned shorts

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Solution