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EE3= 755 practice final 2003.

 

For Computer Arithmetic, Just study the last 2 problems of this practice final.=

 

 

problem 1.  For MI= PS instructions.

LOOP:

0x4= 00000    add r1, r2, r3

        =             beq r0,r0,LOO= P

a)W= rite Machine code for the first instruction.

Hint :

opcode for add is 0 and  fun field value is  20.

b) = when the second instruction is converted to machine co= de,

    wh= at will be the value for “LOOP

sol= )

a)<= o:p>

0x0= 0132020.

b)<= o:p>

beq r0,r0, -2

 

LOOP will be converted to -2..

 

 

 

problem 2. write the  register values after executing fol= lowing instructions.

0x1= 000:        

 

0= x1000

addi r1, r0, 3;       &nbs= p;     

R= 1=3D

R= 2=3D

R= 3=3D

R= 4=3D

R= 31=3D

4=

addi r2, r0, 5;       &nbs= p;     

R= 1=3D

R= 2=3D

R= 3=3D

R= 4=3D

R= 31=3D

8=

s= ub  r3, r1, r2;

R= 1=3D

R= 2=3D

R= 3=3D

R= 4=3D

R= 31=3D

c=

s= ub  r3, r1, r2;

R= 1=3D

R= 2=3D

R= 3=3D

R= 4=3D

R= 31=3D

0= X1010

bne  r3, r0, loop;<= /o:p>

R= 1=3D

R= 2=3D

R= 3=3D

R= 4=3D

R= 31=3D

4=

ori    r1, r2,= 20;

R= 1=3D

R= 2=3D

R= 3=3D

R= 4=3D

R= 31=3D

8=

addi  r6, r0, 0x2000;

R= 1=3D

R= 2=3D

R= 3=3D

R= 4=3D

R= 31=3D

c=

jalr r6;       &nbs= p;            &= nbsp;           &nbs= p;     

<= o:p> 

R= 1=3D

R= 2=3D

R= 3=3D

R= 4=3D

R= 31=3D1024

 

problem 3. Write MIPS program to print  EE3755”;<= /o:p>

hint) data, text, global, system call,

 

sol= ).

 

problem 4. What is wrong with following instructions.

        =           addi r1, r2,0x123456789;

sol= ) too big ..more than 16bits.

problem 5. compile the c code to the MISPs code.

 

        =       if(a > b) d =3D d >>1; else d = =3D d << 1;

        =        register usage  a, $8; b, $9; d , $10;<= /span>

sol= ).

 

problem 6. give examples about DCE, CSE and loop unrolli= ng.        =          

 

problem 7. Write a MIPS code for swap.

 

 

problem 8. Draw  t= he datapath so SW instruction can be done.


 

 


sol= )  add line from rt to memory Din.

Problem 9.   Compute execution time and C= PI.(the figure is wrong..one should be SW, sorry).

The= Finite State Diagram has 10 state.

Clo= ck cycle is 2ns.

state 0 takes 1.5 ns.

state 2-9 takes 2 ns.

Ins= truction mix is this following:

Mem= ory access(LW and SW) is each 5%.

R-t= ype is 70%.

BEQ= is 10 %.

J i= s 10 %.

 

a)Compute single cycle CPI.

b)Compute multi cycle CPI.

c)Designers of new machine found out

    ne= w technology with  1 ns clock cy= cle and each state takes only

    0.= 9 ns except state 9 which takes 1.8 ns.

     c-1) Com= pute single cycle CPI

     c-2) Compute multi cycle CPI.

     c-3) Designers found out  a method = to divide the state 9 into 2 states(  the new 2 stake, state 9-1 and state 9-2) .

        =       state 9-1 takes 1.1 ns.=

        =       state 9-2  takes 1.2 ns.

        =     Is the performance is better or worse?

        =     (Why ).

 


sol= )   a) longest path..so..5 * 2ns =3D 10 ns.

         b) LW  5 * 2 *  0.05 =

             SW  4 * 2= * 0.05

        =      R-type  4 *2 * 0.7

        =      BEQ   2 *2 * 0.1

        =      J    2*2*0.1<= o:p>

 

        =      CPI =3D  <= /span>5 * 2 *  0.05 + 4 * 2 * 0.05+  4 *2 * 0.7

        =             &nb= sp;   +  = 2 *2 * 0.1+    2*2*0.1= ;

         c) worse because to finish 9-1,9-2 , we n= eed 4ns.

 


        =  

 

 

 


 

Problem 10.    Fill the table for SRC2 column.

 

(you will be given the datapath diagram for multicycle control)

 


 

Pro= blem 11: Consider the multiplicative division technique for computing Q=3DA/B. Here = A, B are positive fractions with B being normalized. Also A<B= so that Q be a fraction. If the hardware allows precision of 16 fractio= nal bits, what is the maximum number of iterations that need to be performed be= fore the technique stops?

 

= Justify yo= ur answer.  What is the overall f= actor F in this case?

 

Answer : The maximum number of iterations= to be performed (before the techniques stops) is four, since B is normalized frac= tion, then ½ ≤ B < 1 and therefore B=3D1-δ where 0 < ^= 8; ≤ ½ . The factors involved are F1=3D1+ δ, F2=3D1+ δ2, F3=3D1+ δ4, F4=3D= 1+ δ8.

1st iteration gives B1=3D B×F1 = =3D(1- δ)(1+ δ)=3D1- δ2

2nd iteration gives B2=3D B1×F2 =3D(1- δ2)(1+ δ2)=3D1-= δ4

3rd iteration gives B3=3D B2×F3 =3D(1- δ4)(1+ δ4)=3D1- δ8

4th iteration gives B4=3D B3×F4 =3D(1- δ8)(1+ δ8)=3D1- δ16

 

Sin= ce 0 < δ ≤ ½ then 0 < δ16 ≤ &frac1= 2;16 and thus B4=3D 1- δ16 ≥ 1 - ½1= 6 =3D

(2<= sup>16-1) / 216=3D.111……..111

        =     16 ones

 

The= refore, after at most four iterations the technique stops. The overall factor F is = F=3D F1×F2×F3×F4=3D(1+ δ)( 1+ δ2)( 1+ δ= 4) )( 1+ δ8), and Q≈A×F.

&nb= sp;

Problem12: Consider the following two binary un= signed numbers: A=3Da4a3a2a1a0 and B=3D b2b1b0 where a4 and b= 2 are the most significant bits of A and B while a0 and b0 their least significant bits consider the multiplication P=3DA ×B.

 

a)   &n= bsp; Sho= w the diagram of the 5-by-3 unsigned array multiplier.

 I= f the propagation delay through a 2-input AND gate is DAND and the propagation delay through a Full Adder is DFA, compute the propagation delay through the 5-by-3 unsigned array multiplier.<= /span>

b)   &n= bsp; Wha= t is the cost of the above 5-by-3 multiplier in terms of number of AND gates and num= ber of full adders?


 

 

 <= span class=3DGramE>Answer :

 = ;

a>

 

 

b>Delay=3DDAND + (2+4) DFA =3D DAND + 6DFA

 

c> Cost=3D15 AND gates + 12 Full Adders=

 

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