COA-ITC544 - Computer Architecture and Organization Assignment 1

This document provides a detailed solution to COA-ITC544 Assignment 1, focusing on Computer Architecture and Organization. The assignment covers key concepts such as base conversion, including converting between hexadecimal, base-3, binary, octal, and decimal representations. It also explores the representation of values using 1's complement, 2's complement, and signed magnitude. Furthermore, the solution includes proofs using Boolean algebra identities and De-Morgan's Law to simplify and prove logical expressions related to logic circuits. Desklib provides this and other solved assignments to help students in their studies.

COA-ITC544 Assignment 1
Computer Architecture and Organization
Student name:Wasif Numan
Student ID Number:11640426
Subject Code: ITC544
CSU-Melbourne

COA-ITC544-Assignment 1
Table of Contents
Answer to Question 1:.................................................................................................................2
A.) Value of base x if (152)x = (6A) 16......................................................................................2
b) Conversions.............................................................................................................................2
c) Representation of value..........................................................................................................4
Question 2:.......................................................................................................................................5
a) Prove........................................................................................................................................5
b)Using basic Boolean algebra identities for Boolean variables x, y, and z, for prove...............6
c) Prove:......................................................................................................................................7
1

COA-ITC544-Assignment 1
Answer to Question 1:
A.) Value of base x if (152)x = (6A) 16
The value of base is considered as X
Provided:
(152) x = (6A) 16
Or, X^2 + 5X + 2*X = 6*16 + A
Or, X^2 + 5X + 2*X = 6*16 + 10
X^2 + 5X + 2 = 106
X^2 + 5X- 104 = 0
X^2 + 13X- 8X – 104 = 0
X (X + 13) – 8(X + 13) = 0
(X - 8) (X + 13) = 0
X = 8 and X = -13
Therefore the value of X is 8.
b) Conversions
i) BED16 converting to base-3
= B * 16*16 + E * 16 + D
= 2816 + 224 + 13
= (3053)10
2

COA-ITC544-Assignment 1
(3053)10 =
Therefore,(BED)16 = (11012002)3
ii) 3217 into 2-base (binary) representation
(321)7 = (3 * 72) + (2 * 71) + (1 * 70)
= (162)10
Again, (162)10 =
3

COA-ITC544-Assignment 1
Hence, (162)10= (10100010)2
iii) (1235)10 conversion to octal representation
Solution:
Therefore,(1235)10 = (2323)8
iv) 21.218 conversion to decimal representation
21.218 = (2 * 81) + (1 * 80). (2 * 8-1) + (1 * 7=8-2)
= 17 + 0.25 + 0.015625
= 17.265625
c) Representation of value
i) Highest and lowest value for 1’s complement
Highest Value is 011
Lowest Value is 100
ii) Highest and lowest value for 1’s complement
Highest Value is 011
Lowest Value is 101
iii) Highest and lowest value signed Magnitude
4

COA-ITC544-Assignment 1
Highest Value is 011
Lowest Value is 111
Question 2:
a) Prove
The expression for the above logic diagram is: (a.b)’
Truth tablefor (a.b)’
The expression of the logic diagram
a’ + b’
5

COA-ITC544-Assignment 1
Truth table for a’ + b’
Hence, LHS = RHS (Proved)
b)Using basic Boolean algebra identities for Boolean variables x, y, and z, for prove
The derive expression from the above circuit is provided below:
A’. B’ + A.B = X
The given circuit that can be minimized from above circuit is:
6

COA-ITC544-Assignment 1
c) Prove:
X’ + Y’ + XYZ’
= X’ + Y’ + (X’ + Y’ + Z)’ [by using De-Morgan’s Law]
= (XY (X’ + Y’ + Z))’ [by using De-Morgan’s Law]
= (XX’Y + XYY’ + XYZ)
= (0 + 0 + XYZ)
= (XYZ)’
= X’ + Y’ + Z’ [by using De-Morgan’s Law]
Therefore, X’ + Y’ + XYZ’ = X’ + Y’ + Z’ [PROVED]
7