The test is open-everything with the sole limitation that you neither solicit nor give help while the exam is in progress.

Submit all answers on these exam sheets. No extra sheets are allowed.

1. A 12-bit register can store unsigned values in the range
   
   ______________________ to ______________________
   
   and signed values in the range
   
   ______________________ to ______________________.
2. Complete the following table. All word sizes here are 16-bits.

   	Modular Sum	Signed Saturated Sum	Carry (y/n)	Overflow (y/n)
   7214 + 0326
   3517 + 4BFC
   6519 + F700
   B0BA + 1ACF
   8508 + 92E7
   FFFF + FFFF

3. Express exactly (and I do mean exactly):
   
   
   $2^{50}$ bytes in TiB ______________________________________
   
   
   
   4096 pebibytes in EiB ______________________________________
   
   
   
   1000 bytes in KiB ______________________________________
   
   
   
   $2^{33}+2^{29}$ bytes in GiB ______________________________________
4. Give the single precision IEEE-754 encoding of each of the following:
   
   
   $-3\frac{27}{64} \times 2^{-120}$ ______________________________________
   
   
   
   $-9\frac{5}{8} \times 2^{-140}$ ______________________________________
   
   
   
   $16\frac{11}{16} \times 2^{100}$ ______________________________________
   
5. Is the 32-bit IEEE value 80833AAA normal or denormal? ___________________
6. Express the largest normalized IEEE 754 single-precision (32-bit) value in the form $2^x-2^y$ (that is, find $x$ and $y$).

   
   
   ______________________________________
   

7. For each of the following, give the corresponding sequence of characters (in “U+” format).
   
   
   Medium skin tone woman surfer:
   
   
   __________________________________________________
   Medium skin tone man singer:
   
   
   __________________________________________________
   Flag of American Samoa:
   
   
   __________________________________________________
8. Convert the following codepoints to UTF-8 (Express your answer in hex):

   
   00101101  ____________________________
   
   
   
   000eeeee  ____________________________
   
   
   
   00080000  ____________________________
   

9. Convert the following codepoints to UTF-16LE (Express your answer in hex):

   
   00101101  ____________________________
   
   
   
   000eeeee  ____________________________
   
   
   
   00008000  ____________________________
   

10. Decode each of the following UTF-8 byte sequences into the corresponding character sequences. If a byte sequence is found to be malformed, or decodes into non-characters, decode as much of it as you can (that is, up until the error) and then state what is wrong with the sequence.

    
    
    33 C2 A9 E3 80  ____________________________
    
    
    
    E9 A3 90 F9 80 80 B1 20  ____________________________
    
    
    
    D9 B1 F0 80 92 C5  ____________________________
    

11. Given a 32-bit word that is assumed to contain an unsigned integer, give a logic operation that will perform each of the following tasks:

    Complement the middle four bits _____________________________________
    
    

    Replace it with its value mod 512 ________________________________________
    
    

    Replace it with the largest multiple of 128 less than or equal to itself
    
    ______________________________________________

12. Give a truth table for $A(\overline{B \oplus C})$

    A   B   C
    ----------------------
    0   0   0
    0   0   1
    0   1   0
    0   1   1
    1   0   0
    1   0   1
    1   1   0
    1   1   1
    

13. Rewrite the formula in the previous problem to use NAND operators only.

    
    
    ______________________________________________
    

14. Suppose that address 7 in the simple computer’s memory was found to contain the word 30000A003. How is this interpreted as an instruction? ____________________________ How is it interpreted as data? ____________________________.
15. What does the instruction sequence STORE 50 / XOR 50 do to the accumulator? (Don’t just say “stores it in address 50 then xors it with the contents of address 50”; talk of its effect at a high level)
    
    
    ______________________________________________
16. What does the following code sequence do? (Again, answer at a high-level):

        LOAD Y        Answer: ___________________________________
        SUB  X
        JGZ  L1       ___________________________________________
        LOAD Y
        JUMP L2       ___________________________________________
    L1: LOAD X
    L2: OUT  30       ___________________________________________
    

17. Why is it that “strings are hard” in a systems programming language like C?
    
    _______________________________________________________________________________
    
    _______________________________________________________________________________
18. Here is a C function that makes a copy of string:

    char* duplicate(char* s) {
        int len = strlen(s);
        char* t = malloc(len + 1);
        for (int i = 0; i <= len; i++) {t[i] = s[i];}
        return t;
    }
    

    This works (assuming you included all the right things). Suppose you changed the line declaring t to be char t[len+1];. Why is that horrifying and wrong?
    
    _______________________________________________________________________________
    
    _______________________________________________________________________________

19. Write a C function that returns the sum of squares of an array of doubles. The array is passed to the function.