cs501 Assignment 2 solution file fall 2021
Advance Computer Architecture(CS501)
Assignment # 02
Fall 2021

Question no 1:

Write an RTL description for each of the below given Falcon-A instructions.

Instruction	RTL Description
DIV R2, R3, R1	R[2]←R[0] © R[3]/R[1],R[0]← © R[0] ©R[3]%R[1]
LOAD R2, [R3 + 10]	R[1] ←M[R[3]+10]
HALT	Halt
SHIFTL R3, R2, 6	R[3]<15..0> ← 6@0) ©R[2]<(15..6)
JZ R2, [15]	(R[2]=0): PC ←PC+15;

Question no 2:

Complete the below given table for given Falcon-A Instructions:

Instruction	Op-Code value	Machine Code	ra	rb	rc	c1	c2
DIV R2, R3, R1	5	00101(2A64h)	R2	R3	R1	--	--
LOAD R2, [R3 + 10]	29	011101(EA6Ah)	R2	R3	--	10	--
HALT	31	011111(F8h)	--	--	--	--	--
SHIFTL R3, R2, 6	12	001100(6386h)	R3	R2	--	6	--
JZ R2, [15]	19	010011(9A0Fh)	R2	--	--	--	[15]

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cs502 Assignment No. 02 Fall 2021 Solution file CS502- Design and Analysis of Algorithms
Assignment No. 02
Fall 2021
CS502- Design and Analysis of Algorithms

Question no 1:

Following is the tree diagram of a max heap. You are required to delete node 50 from the given max heap tree, apply heapify procedure and then show only the final max heap tree. No need to show the intermediate steps.

Solution:

Question No 2:

Following is the tree diagram of a min-heap. Insert node 2 in the given min-heap tree, apply the heapify procedure, and show only the final min-heap tree. No need to show the intermediate steps.

Solution:

Question no 3:

The following is the array representation of six elements at its initial stage. You are required to sort this array using the Quicksort technique.

p					r
8	3	5	9	6	2
q	s

Solution:

Given Array

p r

q s

Iteration 1:

p r

i j x

p r

i j x

p r

i j x

p r

i j x

p r

i j x

p r

i jx

p r

Iteration 2:

p r

i j x

p r

i j x

p r

i j x

p r

i j x

p r

i jx

p r

Iteration 3:

p r

i j x

p r

i j x

p r

i jx

p r

Iteration 4:

p r

i j x

p r

i j x

p r

Final sorted array using quick sort algorithm

Question no 4:

Below is a code snippet that calculates prefix averages by keeping a running sum. It takes the average of all "previous" values. It's typically used to calculate the prefix average for each position in an array. In financial applications, the prefix average is extremely useful. You are required to find the time complexity with respect to the worst case.

pAverages(Z,n)
Arr = new array of n integers
b=0
for j=0 to n-1 do
b=b+Z[j]
Arr[j]=b/(j+1)
return Ar

Solution:

Cost	Time complexity
D1	1
D2	1
D3	1
D4	N
D5	n-1
D6	n-1
D7	1

Time complexity in worst case O(n)

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cs501 Assignment 2 solution file fall 2021
Advance Computer Architecture(CS501)
Assignment # 02
Fall 2021

Question no 1:

Write an RTL description for each of the below given Falcon-A instructions.

Instruction	RTL Description
DIV R2, R3, R1	R[2]←R[0] © R[3]/R[1],R[0]← © R[0] ©R[3]%R[1]
LOAD R2, [R3 + 10]	R[1] ←M[R[3]+10]
HALT	Halt
SHIFTL R3, R2, 6	R[3]<15..0> ← 6@0) ©R[2]<(15..6)
JZ R2, [15]	(R[2]=0): PC ←PC+15;

Question no 2:

Complete the below given table for given Falcon-A Instructions:

Instruction	Op-Code value	Machine Code	ra	rb	rc	c1	c2
DIV R2, R3, R1	5	00101(2A64h)	R2	R3	R1	--	--
LOAD R2, [R3 + 10]	29	011101(EA6Ah)	R2	R3	--	10	--
HALT	31	011111(F8h)	--	--	--	--	--
SHIFTL R3, R2, 6	12	001100(6386h)	R3	R2	--	6	--
JZ R2, [15]	19	010011(9A0Fh)	R2	--	--	--	[15]

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cs502 Assignment No. 02 Fall 2021 Solution file CS502- Design and Analysis of Algorithms
Assignment No. 02
Fall 2021
CS502- Design and Analysis of Algorithms

Question no 1:

Solution:

Question No 2:

Following is the tree diagram of a min-heap. Insert node 2 in the given min-heap tree, apply the heapify procedure, and show only the final min-heap tree. No need to show the intermediate steps.

Solution:

Question no 3:

The following is the array representation of six elements at its initial stage. You are required to sort this array using the Quicksort technique.

p					r
8	3	5	9	6	2
q	s

Solution:

Given Array

p r

q s

Iteration 1:

p r

i j x

p r

i j x

p r

i j x

p r

i j x

p r

i j x

p r

i jx

p r

Iteration 2:

p r

i j x

p r

i j x

p r

i j x

p r

i j x

p r

i jx

p r

Iteration 3:

p r

i j x

p r

i j x

p r

i jx

p r

Iteration 4:

p r

i j x

p r

i j x

p r

Final sorted array using quick sort algorithm

Question no 4:

pAverages(Z,n)
Arr = new array of n integers
b=0
for j=0 to n-1 do
b=b+Z[j]
Arr[j]=b/(j+1)
return Ar

Solution:

Cost	Time complexity
D1	1
D2	1
D3	1
D4	N
D5	n-1
D6	n-1
D7	1

Time complexity in worst case O(n)

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cs501 Assignment 2 solution file fall 2021
Advance Computer Architecture(CS501)
Assignment # 02
Fall 2021

Question no 1:

Write an RTL description for each of the below given Falcon-A instructions.

Instruction	RTL Description
DIV R2, R3, R1	R[2]←R[0] © R[3]/R[1],R[0]← © R[0] ©R[3]%R[1]
LOAD R2, [R3 + 10]	R[1] ←M[R[3]+10]
HALT	Halt
SHIFTL R3, R2, 6	R[3]<15..0> ← 6@0) ©R[2]<(15..6)
JZ R2, [15]	(R[2]=0): PC ←PC+15;

Question no 2:

Complete the below given table for given Falcon-A Instructions:

Instruction	Op-Code value	Machine Code	ra	rb	rc	c1	c2
DIV R2, R3, R1	5	00101(2A64h)	R2	R3	R1	--	--
LOAD R2, [R3 + 10]	29	011101(EA6Ah)	R2	R3	--	10	--
HALT	31	011111(F8h)	--	--	--	--	--
SHIFTL R3, R2, 6	12	001100(6386h)	R3	R2	--	6	--
JZ R2, [15]	19	010011(9A0Fh)	R2	--	--	--	[15]

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cs502 Assignment No. 02 Fall 2021 Solution file CS502- Design and Analysis of Algorithms
Assignment No. 02
Fall 2021
CS502- Design and Analysis of Algorithms

Question no 1:

Solution:

Question No 2:

Following is the tree diagram of a min-heap. Insert node 2 in the given min-heap tree, apply the heapify procedure, and show only the final min-heap tree. No need to show the intermediate steps.

Solution:

Question no 3:

The following is the array representation of six elements at its initial stage. You are required to sort this array using the Quicksort technique.

p					r
8	3	5	9	6	2
q	s

Solution:

Given Array

p r

q s

Iteration 1:

p r

i j x

p r

i j x

p r

i j x

p r

i j x

p r

i j x

p r

i jx

p r

Iteration 2:

p r

i j x

p r

i j x

p r

i j x

p r

i j x

p r

i jx

p r

Iteration 3:

p r

i j x

p r

i j x

p r

i jx

p r

Iteration 4:

p r

i j x

p r

i j x

p r

Final sorted array using quick sort algorithm

Question no 4:

pAverages(Z,n)
Arr = new array of n integers
b=0
for j=0 to n-1 do
b=b+Z[j]
Arr[j]=b/(j+1)
return Ar

Solution:

Cost	Time complexity
D1	1
D2	1
D3	1
D4	N
D5	n-1
D6	n-1
D7	1

Time complexity in worst case O(n)

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