Computer Architecture Assignment: Number Systems and Logic Circuits

This assignment delves into fundamental concepts of computer architecture, focusing on number systems, base conversions, and logic gate simplification. It begins by determining the value of X in a base conversion problem, followed by converting numbers between different bases such as base-16, base-3, base-2, octal, and decimal. The assignment further explores the representation of negative numbers using one's complement, two's complement, and signed magnitude in a 3-bit word size computer. Finally, it covers Boolean algebra, demonstrating the equivalence of logical expressions and providing a minimized circuit diagram, showcasing practical application of theoretical concepts. Desklib provides students access to this and many other solved assignments.

Running head: COMPUTER ARCHITECTURE
COMPUTER ARCHITECTURE
Name of Student-
Name of University-
Author’s Note-

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Answers of Question 1:
a) Determining the value of X:
(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 calculated value for X is 8.
(152)8= (6A) 16
b) Conversions:
i) BED16 conversion to base-3
BED = (B * 162) + (E * 161) + (D * 160)
= 2816 + 224 + 13
= (3053)10
(3053)10 =

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So, after conversion BED16 = (11012002)3
ii) 3217 converting into 2-base
3217 = (3 * 72) + (2 * 71) + (1 * 70)
= (162)10
Again, (162)10 =
After conversion: (162)10 = (10100010)2

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iii) 1235 conversion into octal representation
After converting, (1235) = (2323)8
iv) 21.218 conversion to decimal representation
21.218 = (2 * 81) + (1 * 80). (2 * 8-1) + (1 * 7=8-2)
= 17 + 0.25 + 0.015625
= 17.265625
c) i) In a 3 bit word size computer, the negative number that is possible for one’s complement
number = 100
In a 3 bit word size computer, the positive number that is possible for one’s complement number
= 011
ii) In a 3 bit word size computer, the negative number that is possible for two’s complement
number = 101

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In a 3 bit word size computer, the positive number that is possible for two’s complement number
= 011
iii) In a 3 bit word size computer, the negative number that is possible for signed magnitude
number = 111
In a 3 bit word size computer, the positive number that is possible for signed magnitude number
= 011
Answers of Question 2:
a) From given L.H.S
a b c d
0 0 0 1
0 1 0 1
1 0 0 1
1 1 1 0
From given R.H.S.

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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
From the above result, it can be clear that the result of L.H.S. is equal to R.H.S.
b) Minimized Circuit Diagram from the given diagram can be:
c) X’ + Y’ + XYZ’
= X’ + Y’ + (X’ + Y’ + Z)’ [From, De-Morgan Law]
= (XY (X’ + Y’ + Z))’ [From, De-Morgan Law]

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= (XX’Y + XYY’ + XYZ)
= (0 + 0 + XYZ)
= (XYZ)’
= X’ + Y’ + Z’ [From, De-Morgan Law]
[Hence, PROVED]

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micro-ring resonator structures. Optical and Quantum Electronics, 48(10), 477.
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