ITC544: Data Representation and Digital Logic in Computer Architecture

This assignment solution delves into the fundamental concepts of data representation and digital logic within the context of computer organization and architecture (ITC544). It includes detailed solutions for converting numbers between different bases (decimal, binary, octal, hexadecimal, and base-3), performing calculations with one's and two's complements, and simplifying Boolean expressions using truth tables and De-Morgan's laws. The assignment demonstrates the conversion of hexadecimal and base-7 numbers to decimal and binary, showcasing the methods for representing numerical values in various formats. Furthermore, it explores digital logic by analyzing logic diagrams, constructing truth tables, and simplifying Boolean expressions to their minimal forms. Desklib offers this document as a valuable resource for students seeking to enhance their understanding of these core computer science principles, alongside a wide array of past papers and solved assignments.

Running head: COMPUTER ORGANIZATION AND ARCHITECTURE
Assignment 1: Data Representation and Digital Logic
Subject Code (ITC544)
Student Name
Student ID
Name of the University
Author’s Note

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Table of Contents
Answer to Question 1:.....................................................................................................................2
Answer to Question 2:.....................................................................................................................5
Bibliography....................................................................................................................................8

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Answer to Question 1:
a. Determination of the value of x,
if (152)x = (6A)16
=> x2 + 5x + 2*x = 6 * 16 +A
=> x2 + 5x + 2*x = 6 * 16 +10
=> x2 + 5x + 2 = 106
=> x2 + 5x -104 = 0
=> x2 + 13x – 8x -104
=> x(x+13) -8 (x+13) = 0
=> (x-8) (x+13) = 0
Thus, x =8 or, -13
Discarding the negative value we get that the value of x = 8
b. Conversion
i) 0xBED into 3-base representation
=> B * 16 * 16 + E * 16 + D
=> 2816 + 224 + 13
=> (3053)10
3 3053

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3 1017 2
3 339 0
3 113 0
3 37 2
3 12 1
3 4 0
3 1 1
Thus, (BED)16 = (11012002)3
ii) 3217 into 2-base (binary) representation
=> (321)7 = (3 * 72) + (2 * 71) + (1 * 70)
=> (162)10
Thus, (162)10 =>
2 162
2 81 0
2 40 1
2 20 0
2 10 0
2 5 0
2 2 1
2 1 0
Therefore, (162)10 = (10100010)2

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iii) 1235 into octal representation
8 1235
8 154 3
8 19 2
8 2 3
Therefore, (1235)10 = (2323)8
iv) 21.218 into decimal representation
=> 21.218 = (2 * 81) + (1 * 80) + (2 * 8-1) + (1 * 8-2)
=> 16 + 0.25 + 0.015625
=> 17.26562510
c. i) One's complement
Lowest value (negative number) = 100
Highest value (positive number) = 011
ii) Two's complement
Lowest value (negative number) = 101
Highest value (positive number) = 011
iii) Signed Magnitude
Lowest value (negative number) =111

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Highest value (positive number) = 011
Answer to Question 2:
a.
The expression for the logic diagram is: (a.b)’
The following is the truth table of the first expression
A B a.b (a.b)’
0 0 0 1
0 1 0 1
1 0 0 1
1 1 1 0
The expression of the logic diagram can be given as:
=> a’ + b’

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The following is the truth table of the second expression
a b a’ b’ a’ + b’
0 0 1 1 1
0 1 1 0 1
1 0 0 1 1
1 1 0 0 0
Therefore, First Expression = Second Expression
b.
The following expression is derived from the above diagram:
A’. B’ + A.B = X
It can be simplified as follows:

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c.
X’ + Y’ + XYZ’
= X’ + Y’ + (X’ + Y’ + Z)’ [ By applying De-Morgan’s Law]
= (XY (X’ + Y’ + Z))’ [By applying De-Morgan’s Law]
= (XX’Y + XYY’ + XYZ)
= (0 + 0 + XYZ)
= (XYZ)’
= X’ + Y’ + Z’ [By applying De-Morgan’s Law]
Hence, X’ + Y’ + XYZ’ = X’ + Y’ + Z’ [Hence Proved]

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Bibliography
Harris, S., & Harris, D. (2015). Digital Design and Computer Architecture: ARM Edition.
Morgan Kaufmann.
Null, L., & Lobur, J. (2014). The essentials of computer organization and architecture. Jones &
Bartlett Publishers.