Computer Organization and Architecture Problems

This computer organization and architecture assignment focuses on various concepts including number system representation (ones' complement, two's complement, signed magnitude, unsigned magnitude), binary to decimal and hexadecimal conversions, Boolean algebra simplification using distributive law and logic gates, and the expression for student pass rates based on different learning methods. The provided solutions demonstrate step-by-step calculations and circuit diagram implementation.

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

1COMPUTER ORGANIZATION AND ARCHITECTURE
Question 1.
(a)
I. In a computer of 8 bit, smallest negative of one’s compliment is -127 and largest number
is 127.
II. In a computer of 8 bit, smallest negative of two’s compliment is -128 and largest number
is 127.
III. In a computer of 8 bit, smallest negative of signed magnitude is -127 and largest number
is 127.
IV. In a computer of 8 bit, smallest negative of unsigned magnitude is 0 and largest number
is 255.
(b)
I. (5AB)16 = (2653)8
II. (101101.101)2 = (45.625)10
III. (12348)10 = (1100000111100)2
IV. (679810)10 = (133223220)5
V. (976.6310)10 = (1111010000.10100)2
VI. (1001001011)2 = (24B)16
VII. (10011110) = -(98)10
Question 2:
(a) X’(X+Y)+(XX+Y)(Y’+X)=Y+X
L.H.S. – X’(X+Y) + XXY’+ XXX+ YY’+ XY [Distributive law]
= X’X + X’Y + XXY’+ XXX + YY’+ XY [Distributive law]

2COMPUTER ORGANIZATION AND ARCHITECTURE
= 0 + X’Y + XY’ + X + 0 + XY [Since, X’X = 0 AND XX = X]
= X’Y + XY’ + X + XY
= X’Y + XY’ + X (1 + Y)
= X’Y + XY’ + X [Since, 1 + Y = 1]
= X’Y + X (Y’ + 1)
= (X + X’) (X + Y)
= (X + Y) [Since, X + X’ = 1] = R.H.S.
(b) Let, the Assignment, Blog, Discussion Forum and Quiz be A, B, C, and D. P be the
possibility of students who can pass the exam.
So, the truth table will be:
A B C D P
0 0 0 0 0
0 0 0 1 0
0 0 1 0 0
0 0 1 1 0
0 1 0 0 0
0 1 0 1 0
0 1 1 0 0
0 1 1 1 0
1 0 0 0 0
1 0 0 1 0
1 0 1 0 0
1 0 1 1 1

3COMPUTER ORGANIZATION AND ARCHITECTURE
1 1 0 0 0
1 1 0 1 1
1 1 1 0 1
1 1 1 1 1
The expression for students passing in the following table will be
AB’CD + ABC’D + ABCD’ + ABCD
Minimizing the equation we get,
A [D (B’C + BC) + BCD’]
The circuit diagram for the equation is