15-213 Fall 2007
Midterm Exam Solutions

There were two versions of the exam: version A and version B.  You can tell
the difference as follows: on question 5, if "status_array" (the last line
of C code) was declared with 10 elements, then you had version A; if it was
declared with 20 elements, then you had version B.


=====================================================================

           Solutions to Midterm Exam Version A

=====================================================================


*********
Problem 1
*********

((~(ux>>31)) & ux) != ux           | False (MSB=0)       
x >= 0 ) => ((x ^ (x>>31))) <= 0   | False (x>0)         
((-(!x)) & x) == 0                 | True                
x < 0 => ((~x)+1) > 0		   | False (TMin)        
x > 0 => (x+ux) > 0U               | True                
x < 0 => (x-1) < 0                 | False (TMin)        
x >= 0 =>  -(((~x) >> 1) + 1) > 0  | False (0, 1, TMax)  
((~(x>>31))+1) == (x<0)            | True                


*********
Problem 2
*********

Value:    Sign Bit:  Exponent:  Significand:
-1/1024   1          0000       0001
248       0          1110       1111
          1          1001       0100
          1          0010       1000
          0          0101       1001
          0          1000       0111


*********
Problem 3
*********

array[0] != 1
0
1
< n
i++
array[i] != (array[i-1]*2)
0
1


*********
Problem 4
*********

7x
3y
3
7

*********
Problem 5
*********

12, 0
16, 4
160, 70

*********
Problem 6
*********

CT CT CT CI CI CO CO CO

b, 2 hits

*********
Problem 7
*********

ABCBEDE
ABCEBDE

=====================================================================

           Solutions to Midterm Exam Version B

=====================================================================


*********
Problem 1
*********

x > 0 => (x+ux) > 0U                | True                
x >= 0 => -(((~x) >> 1) + 1) > 0    | False (0, 1, TMax)    
((~(ux>>31)) & ux) != ux	    | False (MSB=0)         
((-(!x)) & x) == 0		    | True                
x < 0 => ((~x)+1) > 0		    | False (TMin)          
x < 0 => (x-1) < 0		    | False (TMin)          
((~(x>>31))+1) == (x<0)		    | True                
x >= 0 => ((x ^ (x>>31))) <= 0	    | False (x>0)           

*********
Problem 2
*********

Value:    Sign Bit:  Exponent:  Significand:
-1/1024   1          0000       0001
248       0          1110       1111
          1          1001       0100
          1          0010       1000
          0          0101       1001
          0          1000       0111


*********
Problem 3
*********

array[0] != 1
0
1
< n
i++
array[i] != (array[i-1]*2)
0
1

*********
Problem 4
*********

31x
3y
3
31

*********
Problem 5
*********

16, 4
12, 0
320, 140


*********
Problem 6
*********

CT CT CT CI CI CO CO CO

g, 2 hits

*********
Problem 7
*********

ABCBEDE
ABCEBDE