Data Representation and Digital Logic - Assignment 1

This assignment covers topics like data representation, digital logic, one's complement, two's complement, signed magnitude, and logic diagrams.

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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COMPUTER ORGANIZATION AND ARCHITECTURE
Table of Contents
Answer to Question 1:.....................................................................................................................2
Answer to Question 2:.....................................................................................................................5
Bibliography....................................................................................................................................8

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COMPUTER ORGANIZATION AND ARCHITECTURE
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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COMPUTER ORGANIZATION AND ARCHITECTURE
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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COMPUTER ORGANIZATION AND ARCHITECTURE
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.