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 =
span>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 =
sub>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=
sub> =3D DAND
+ 6DFA
c> Cost=3D15 AND gates + 12 Full Adders=
=
p>
------=_NextPart_01C3B59F.12748700
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