Question

For each of the following propositions, write in all comparisons that make it always true among the four possibilities:

< > == !=

If none are guaranteed to hold, please indicate that explicitly by marking it with an X. Assume the variables are declared with int x,y; and initialized to some unknown values. You may assume that int’s are 32 bits wide, char’s are 8 bits wide and that right shift is arithmetical on signed numbers and logical on unsigned numbers.

1. If x > y then y ? 0

2. If x < 0 then x+1 X 0

3. If x > 0 then x+1 ? 0

4. If (x >> 31) < 0 then x ? 0

5. If ((x > 31) < 0 then x & 1 ? 0

6. If x > y then (unsigned) x ? y

7. If ((unsigned char)x >> 1) < 64 then (char) x ? 0

Answer 1

Answer :

Let x=5,y=3

1) if x>y the y?0

Ans: 5 > 3 then 3 >0 so

x > y then y > 0

Let x=-2

2) if x < 0 then x+1 X 0

Ans : -2 < 0 then -2+1 < 0

  x < 0 then x+1 < 0

Let x=2

3. If x > 0 then x+1 ? 0

Ans : 2>0 then 2+1 > 0

x > 0 then x+1 >0

Let x=-15

4. If (x >> 31) < 0 then x ? 0

Ans: (-15>>31)=-1

-1< 0 then x < 0

5. If ((x > 31) < 0 then x & 1 ? 0

Ans : Let x=32

((x > 31) < 0 then x & 1 == 0

6. If x > y then (unsigned) x ? y

Ans : x > y then (unsigned) x > y

7. If ((unsigned char)x >> 1) < 64 then (char) x ? 0

Ans : Let x= 34

x>>1 => 17 < 64 then x>0