MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01C3B59F.27D16E10" This document is a Web archive file. If you are seeing this message, this means your browser or editor doesn't support Web archive files. For more information on the Web archive format, go to http://officeupdate.microsoft.com/office/webarchive.htm ------=_NextPart_01C3B59F.27D16E10 Content-Location: file:///C:/6457A1D1/final_problem1.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" New…

EE3= 755 practice final 2003.

 

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

 

 

problem 1.  Write MIPS machine code fo= r the following instructions.

LOOP:

0x4= 00000    add r1, r2, r3

        =             beq r0,r0,LOO= P

Hint :

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

opcode for beq is 4.

 

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

<= o:p> 

addi r2, r0, 5;       &nbs= p;     

R= 1=3D

R= 2=3D

R= 3=3D

R= 4=3D

R= 31=3D

<= o:p> 

s= ub  r3, r1, r2;

R= 1=3D

R= 2=3D

R= 3=3D

R= 4=3D

R= 31=3D

<= o:p> 

s= ub  r3, r1, r2;

R= 1=3D

R= 2=3D

R= 3=3D

R= 4=3D

R= 31=3D

<= o:p> 

bne  r3, r0, loop;<= /o:p>

R= 1=3D

R= 2=3D

R= 3=3D

R= 4=3D

R= 31=3D

<= o:p> 

ori    r1, r2,= 20;

R= 1=3D

R= 2=3D

R= 3=3D

R= 4=3D

R= 31=3D

<= o:p> 

addi  r6, r0, 0x2000;

R= 1=3D

R= 2=3D

R= 3=3D

R= 4=3D

R= 31=3D

<= o:p> 

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

<= o:p> 

R= 1=3D

R= 2=3D

R= 3=3D

R= 4=3D

R= 31=3D

 

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

hint) data, text, global, system call,

 

problem 4. What is wrong with following instructions.

        =           addi r1, r2,0x123456789;

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>

 

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.


 

 


 

Problem 9.   Compute execution time and C= PI.

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 10%.

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 ).

        =    

 

 

 


 

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&= lt;B so that Q be a fraction. If the hardware allows precision of 16 fractional bits, what is the maximum number of iterations that need to be performed before 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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