EE380 Assignment 4 Solution

1. 50% 50% A single-precsion floating-point value for the MIPS processor is encoded in the IEEE-compliant format illustrated below (the LSB is on the right). Given this encoding, using only MIPS integer instructions, write a function that will compute the absolute value of a floating-point number, i.e., x=abs(y);. Hints: use the fact that negative and positive float values differ only in the Sign bit, and test your routine using SPIM before you submit it.

   
   

   #### # # Float abs # # x = abs(y) # just zero top bit using and # .text .globl myfabs myfabs: la $t0, y lw $t0, 0($t0) li $t1, 0x7fffffff and $t0, $t0, $t1 la $t1, x sw $t0, 0($t1) jr $ra # return

2. 100% We all know that floating point arithmetic is subject to roundoff errors. What about how floating point addition is implemented makes it inherently more subject to loss of accuracy than floating-point multiplication?
   Multiplication does not have the initial step that adjusts the operands to have the same exponent; that adjustment in addition (denormalization) essentially shifts mantissa bits from the value with the lower exponent into oblivion.

3. 
   
   100% In the single-cycle design shown in the above (rather large and very familiar) figure, which of the following signals is a "don't care" when executing a MIPS beq instruction?
   Branch
   RegDst
   ALUSrc
   MemRead
   RegWrite
4. 100% How would you build the "Shift left 2" function unit shown in the single-cycle design in the figure above? Answer in terms of the logic functions relating input bits I0-I31 to output bits O0-O31.
   O0 = 0 O1 = 0 O(k) = I(k-2) for k in 2..31 i.e., no logic -- just a wiring pattern
5. 100% Which of the following techniques for implementing control logic for a single-cycle design (like that given in Chapter 5) is most likely to yield the circuit that operates with the smallest delay?
   Lookup Table (ROM)
   Random Logic
   Gate Array
6. 100% In multiplying an integer, X, by 17 using the basic shift-and-add algorithms discussed in class and in the book, what is the minimum number of additions that must be performed? Show the values that are added (hint: use (X<<Y) to represent the value of X shifted by Y bit positions).
   17 is 16 + 1, thus: X*17 = (X*16)+X = (X<<4)+X That's just one add... unless you think of it as: (X<<4) + (X<<0) + 0 In which case it's two.
7. 
   
   100% In the single-cycle design shown in the above (rather large and very familiar) figure, suppose that ALUSrc=0 and MemRead=1. Which of the following MIPS instructions might be executing?
   Sw $t0,4($t1)
   Lw $t0,4($t1)
   Ori $t0,$t1,2
   Add $t0,$t1,$t2
   None of the above instructions is consistent with the stated signal values

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