Solved Homework: Computer Organization and Architecture Problem

This document provides a detailed solution to a homework assignment on computer organization and architecture. It covers various topics, including number base conversions (decimal, binary, octal, hexadecimal), 1's and 2's complement representation, signed magnitude, and Boolean algebra simplification using DeMorgan's Law. The solution includes step-by-step explanations for converting numbers between different bases, determining maximum and minimum values in different complement representations, and simplifying logical expressions. The document also includes truth tables and logic diagrams to illustrate the concepts and solutions. Desklib offers a wide range of solved assignments and study resources for students.

Running head: COMPUTER ORGANIZATION AND ARCHITECTURE
Computer Organization and Architecture
Name of Student:
Name of University:
Author’s Note

1COMPUTER ORGANIZATION AND ARCHITECTURE
Answers to question number 1:
a)
Let us consider the base to be Y,
Given,
(152) Y = (6A) 16
Or, Y2 + 5Y + 2*Y = 6*16 + A
Or, Y2 + 5Y + 2*Y = 6*16 + 10
Y2 + 5Y + 2 = 106
Y2 + 5Y- 104 = 0
Y2 + 13Y- 8Y – 104 = 0
Y (Y + 13) – 8(Y + 13) = 0
(Y - 8) (Y + 13) = 0
Y = 8 and Y = -13
Hence, the value of Y is 8.
The value of the base is 8.
b)
Conversions:

2COMPUTER ORGANIZATION AND ARCHITECTURE
i) BED16 converting to base-3
= B * 16*16 + E * 16 + D
= 2816 + 224 + 13
= (3053)10
(3053)10 =
So, (BED)16 = (11012002)3
ii)
(321)7 = (3 * 72) + (2 * 71) + (1 * 70)
= (162)10
Again, (162)10 =

3COMPUTER ORGANIZATION AND ARCHITECTURE
Hence, (162)10 = (10100010)2
iii) (1235)10 conversion to octal representation
Hence, (1235)10 = (2323)8
iv) (21.21)8 conversion to decimal representation
21.218 = (2 * 81) + (1 * 80). (2 * 8-1) + (1 * 7=8-2)
= 17 + 0.25 + 0.015625
= 17.265625

4COMPUTER ORGANIZATION AND ARCHITECTURE
c)
i) 1's complement
Maximum Value is 011
Minimum Value is 100
ii) 2's complement
Maximum Value is 011
Minimum Value is 101
iii) Signed Magnitude
Maximum Value is 011
Minimum Value is 111
Answers of Question 2:
a)
The expression for the logic diagram is: (a.b)’
Truth table of the expression:

5COMPUTER ORGANIZATION AND ARCHITECTURE
The logic diagram can be expressed as
a’ + b’
the truth table of the given expression
Hence, LHS = RHS
b)

6COMPUTER ORGANIZATION AND ARCHITECTURE
The derived expression from the given diagram is provided below:
A’. B’ + A.B = X
The simplified from of the provided diagram is provided below:
c) 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)’

7COMPUTER ORGANIZATION AND ARCHITECTURE
= X’ + Y’ + Z’ [ by using De-Morgan’s Law]
Hence, X’ + Y’ + XYZ’ = X’ + Y’ + Z’ [PROVED]

8COMPUTER ORGANIZATION AND ARCHITECTURE
Bibliography
Bhattacharya, P. (2017). Modelling Strategic Alignment of Business and IT through
Enterprise Architecture: Augmenting Archimate with BMM. Procedia Computer Science, 121,
80-88.
Tanenbaum, A. S. (2016). Structured computer organization. Pearson Education India.