ITC544 - Data Representation and Digital Logic Complete Assignment

This assignment solution covers fundamental concepts of data representation and digital logic, addressing questions related to number systems and logic gates. The first question involves determining the base of a number system and converting numbers between different bases such as hexadecimal, ternary, binary, octal, and decimal. It also explores 1's complement, 2's complement, and signed magnitude representations. The second question focuses on digital logic, including deriving expressions from logic diagrams, creating truth tables, simplifying Boolean expressions using De-Morgan's Law, and identifying logic gates. The solution provides detailed steps and explanations for each problem, offering a comprehensive understanding of the subject matter.

Running head: DATA REPRESENTATION AND DIGITAL LOGIC
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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DATA REPRESENTATION AND DIGITAL LOGIC
Table of Contents
Question 1:.......................................................................................................................................2
Question 2:.......................................................................................................................................5
Bibliography....................................................................................................................................8

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DATA REPRESENTATION AND DIGITAL LOGIC
Question 1:
a. Determination of the value of base x from the following equation
(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 = 0
=> x(x+13) -8 (x+13) = 0
=> (x-8) (x+13) = 0
Therefore, x =8 or, -13
We would consider the positive value as the value of the base x = 8
b. Convert the followings
i) 0xBED into 3-base representation
=> B * 16 * 16 + E * 16 + D
=> 2816 + 224 + 13
=> (3053)10
3 3053

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DATA REPRESENTATION AND DIGITAL LOGIC
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
Therefore, (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

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DATA REPRESENTATION AND DIGITAL LOGIC
Thus, (162)10 = (10100010)2
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) 1's complement
Lowest value = 100
Highest value = 011
ii) Two's complement
Lowest value = 101
Highest value = 011

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DATA REPRESENTATION AND DIGITAL LOGIC
iii) Signed Magnitude
Lowest value =111
Highest value = 011
Question 2:
a.
The expression obtained from the logic diagram = (a.b)’
Truth table for the expression
a b a.b (a.b)’
0 0 0 1
0 1 0 1
1 0 0 1
1 1 1 0

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DATA REPRESENTATION AND DIGITAL LOGIC
The expression obtained from the logic diagram = a’ + b’
The truth table for the above 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, 1st logic diagram = 2nd Logic diagram
b.
The following expression is derived from the above diagram:
A’. B’ + A.B = X
It can be simplified XOR gate:

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DATA REPRESENTATION AND DIGITAL LOGIC
c.
X’ + Y’ + XYZ’
=> X’ + Y’ + (X’ + Y’ + Z)’ (With the application of De-Morgan’s Law)
=> (XY (X’ + Y’ + Z))’ (With the application of De-Morgan’s Law)
=> (XX’Y + XYY’ + XYZ)
=> (0 + 0 + XYZ)
=> (XYZ)’
=> X’ + Y’ + Z’ (With the application of De-Morgan’s Law)
Therefore, X’ + Y’ + XYZ’ = X’ + Y’ + Z’ [Proved]

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DATA REPRESENTATION AND DIGITAL LOGIC
Bibliography
Comer, D. (2017). Essentials of computer architecture. CRC Press.
Harris, S., & Harris, D. (2015). Digital Design and Computer Architecture: ARM Edition.
Morgan Kaufmann.
Tanenbaum, A. S. (2016). Structured computer organization. Pearson Education India.
Wang, S., & ZHANG, C. (2016). Computer architecture.