Homework 2 (48 points total)

Show your work for full credit.

1. (12 points) Convert numbers from the given integer representation to fill in the following table. Use 8 bits for all answers. Identify where an integer cannot be represented with the asterisk character (*).
   
   

   Sign Magnitude	One's Complement	Two's Complement	Biased-127
   10011010
   	01101011
   		10000000
   			10100010

   
   
   
2. (4 points) What is the IEEE single precision floating point representation for the decimal value 18.7291? Show intermediate steps for partial credit.
   
   
3. (2 points) Give a (brief) decription of what the following SAL program does.
   

   		           .data
   		aaa:       .word   1000
   		bbb:       .word   0
   		ccc:       .word   0
   		newline:   .byte   '\n'
   		str:       .asciiz "The answer is "
   		
   		           .text
   		__start:
   		loop_top:  beq  bbb, aaa, loop_end
   		           add  bbb, bbb, 1
   		           add  ccc, ccc, bbb
   		           b    loop_top
   		loop_end:  puts str
   		           put  ccc
   	 	           put  newline
   		done
   		

4. (8 points) Assume that a memory read or write operation takes 12 nsec (nanoseconds), and processor operations like decode or add take 3 nsec. Show your work in computing how long it takes to execute the following SAL code sequence.

           sub  z, x, y
           add  a, z, y
   

5. (3 points) Labels, addresses, and contents at those addresses are given by the following table.

   label   address   contents
   --------------------------
    v1       15        20
    v2       16        17
    v3       17        -2
    v4       18        -3
   

   Give this complete table, with any changes, after the following SAL code fragment is executed.

           la   v2, v4
           mov  v1, v4
   

6. (2 points) Interpreting 0xC4FB4000 in IEEE single precision, what is the decimal value and the 32-bit binary representation (containing a sign bit, 8-bit exponent field and 23-bit significand)?
7. (2 points) What message is contained in the following hexadecimal digits if interpreted as an ASCII string?

   48 65 6c 70 21 20 49 27 6d 20 74 72 61 70 70 65 64 20
   69 6e 73 69 64 65 20 61 20 63 6f 6d 70 75 74 65 72 21

8. (4 points) Do the following sign magnitude arithmetic. If the result does not fit in 8 bits, write the word OVERFLOW.

    01100011
   +10001101
    --------
   
    10000111
   -11001101
    --------
   

9. (4 points)Do the following two's complement arithmetic. If the result does not fit in 8 bits, write the word OVERFLOW.

    11110011
   +10011101
    --------
   
    10000111 
   -11001101 
    -------- 
   

10. (3 points) Do the following 8-bit two's complement multiplication. Give a 16-bit result.

    
              10100111
          x   11101101
          -------------
    
    

11. (4 points) Show the following unsigned binary division.
    Identify both the quotient and the remaider.

              101011 / 0100 
    

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