Computer Organization and Architecture - Assignment 1 - ITC544

This document presents a solution to a computer organization and architecture assignment (ITC544). The assignment addresses several key concepts, including data representation using IEEE 754 single-precision format and binary conversions. It covers the representation of numbers in signed magnitude, one's complement, and two's complement forms. Furthermore, the assignment includes a practical application of logic circuits, demonstrating how AND, OR, and NOT gates can be used to create a system for controlling the CSU main entrance door. The solution provides a Boolean function and a logic diagram to illustrate the circuit design. Finally, the document includes a proof of a Boolean expression using algebraic manipulation. This resource is designed to help students understand and solve similar problems in computer organization and architecture.

Running head: COMPUTER ORGANIZATION AND ARCHITECTURE
Computer Organization and Architecture
Student Name:
Student ID:
Subject Code: ITC544
Assignment 1: Data Representation and Digital Logic
Author’s Note

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COMPUTER ORGANIZATION AND ARCHITECTURE
Answer to Question 1:
a. Single precision IEEE 754 format- 0 01111110 10100000000000000000000
The MSB is the sign and the middle portion describes the exponent and the last is the
mantissa.
Decimal conversion of the binary digit is 8.125 * 10^-1
b. Let the 5-bit word be 0 1010
i. The Signed magnitude= +10 (Most significant bit-0 [positive] rest 4 bits are magnitude)
ii. One’s complement= 10101 (all the 0’s are replaced by 1 and vice-versa)
iii. Two’s complement= 10110 (1 is added to the one’s complement)
Answer to Question 2:
a.
Magnitude Binary Clock pulse
(p)
1 A B C D E High (+1)
00001
2 00010
3 00011
4 00100
5 00101
6 00110

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COMPUTER ORGANIZATION AND ARCHITECTURE
7 00111
8 01000
9 01001
10 01010
11 01011
12 01100
13 01101 Low (0)
14 01110
15 01111
16 10000
17 10001
18 10010
19 10011
20 10100
21 10101
22 10110
23 10111
24 11000
The Boolean function created for the construction of the logic circuit using the basic logic gates
for activating the CSU main entrance door from 9:00 am to 12:00 pm and after lunch after a time
period of 1:00 pm - 4:00 pm is given below:
AND gate, OR gate and Not gate is used for the creation of the basic circuit diagram.
The logic diagram developed for the system is given as follows:

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COMPUTER ORGANIZATION AND ARCHITECTURE
A'BC'D'EP+A'BC'DE'P+A'BC'DEP+A'BCD'E'P=Q (For clock= +1)
A'BCD'EP’+A'BCDE'P’+A'BCDEP’+AB'C'D'E'=R (For clock=0)
Figure 1: Logic diagram for activating the CSU main entrance door
(Source: Created by the author)
b.
X’Y+XYZ’+Y’+XZ (Y+Y’)

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COMPUTER ORGANIZATION AND ARCHITECTURE
= X’Y+XYZ’+Y’+XZY+XZY’
= X’Y+XY (Z+Z’)+ Y’+XZY’
=X’Y+XY+Y’+XZY’
=Y+Y’+XZY’
=1+XZY’
=1 (PROVED)