ITC544 Computer Organization Assignment - Number Systems and Logic

This document presents a comprehensive solution to an ITC544 Computer Organization assignment. The solution addresses several key concepts, including number system conversions between different bases (binary, hexadecimal, octal, and decimal). The student demonstrates proficiency in convert...Read More

Running head: ITC544 COMPUTER ORGANIZATION
ITC544 COMPUTER ORGANIZATION
Name of Student –
Name of University –
Author’s Note –

1ITC544 COMPUTER ORGANIZATION
Answer to Question 1
a) (152)x= (6A)16
 X2 + (5 * X1) + (2 * X0) = (6 * 161) + (10 * 160)
 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
 X = 8 and X = -13
So, the value of X is 8
b) Conversions
1) BED16 to base 3
BED = (B * 162) + (E * 161) + (D * 160)
= 2816 + 224 + 13
=305310
(3053)10 =

2ITC544 COMPUTER ORGANIZATION
BED16 => (11012002)3
2) 3217 into 2-base
3217 = (3 * 72) + (2 * 71) + (1 * 70)
= (162)10
(162)10 =
(162)10 = (10100010)2
3) 1235 into octal representation

3ITC544 COMPUTER ORGANIZATION
(1235) = (2323)8
4) 21.218 into decimal representation
21.218 = (2 * 81) + (1 * 80). (2 * 8-1) + (1 * 7=8-2)
= 17 + 0.25 + 0.015625
= 17.265625
c) i) One’s Complement lowest number of word size 3 bit = 100
One’s Complement lowest number of word size 3 bit = 011
ii) Two’s Complement lowest number of word size 3 bit = 101
Two’s Complement lowest number of word size 3 bit = 011
iii) Signed Magnitude lowest number of word size 3 bit = 111
Signed Magnitude lowest number of word size 3 bit = 011
Question 2
a) L.H.S

4ITC544 COMPUTER ORGANIZATION
a b c d
0 0 0 1
0 1 0 1
1 0 0 1
1 1 1 0
R.H.S.
a b c d e
0 0 1 1 1
0 1 1 0 1
1 0 0 1 1
1 1 0 0 0

5ITC544 COMPUTER ORGANIZATION
The output of L.H.S. and the output of R.H.S. are equal. Hence, both the
combinational circuits are same.
b) Minimized Circuit Diagram
c) X’ + Y’ + XYZ’
= X’ + Y’ + (X’ + Y’ + Z)’ [De Morgan Law]
= (XY (X’ + Y’ + Z))’ [De Morgan Law]
= (XX’Y + XYY’ + XYZ)
= (0 + 0 + XYZ)
= (XYZ)’
= X’ + Y’ + Z’ [De Morgan Law] [Hence, PROVED]

6ITC544 COMPUTER ORGANIZATION
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