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.