COA-ITC544 Assignment 1 - Desklib

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
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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
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