Data Representation and Logic Conversion

This assignment delves into the fundamentals of data representation in computers. It covers various number systems (binary, octal, decimal, hexadecimal) and their representations. The student demonstrates understanding by converting numbers between these systems and applying Boolean logic to simplify expressions. Additionally, the assignment includes a truth table analysis and circuit diagram design based on a given Boolean expression.

Running head: DATA REPRESENTATION
Data Representation
Name of Student-
Name of University-
Author’s Note-

1DATA REPRESENTATION
Answer to Question 1.
(a).
I. The computer that has word size of 8 bits has one’s compliment range of -127 to 127.
II. The computer that has word size of 8 bits has two’s compliment range of -128 to 127.
III. The computer that has word size of 8 bits has signed magnitude of range of -127 to 127.
IV. The computer that has word size of 8 bits has unsigned magnitude of range of 0 to 255.
(b).
I. (5AB)16 = (2356)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
Answer to Question 2:
(a) X’(X+Y)+(XX+Y)(Y’+X)=Y+X
L.H.S. – X’(X+Y) + XXY’+ XXX+ YY’+ XY [Because of Distributive law]
= X’X + X’Y + XXY’+ XXX + YY’+ XY [Because of Distributive law]
= 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]

2DATA REPRESENTATION
= X’Y + X (Y’ + 1)
= (X + X’) (X + Y)
= (X + Y) [Since, X + X’ = 1] = R.H.S.
(b) Suppose, Assignment, Blog, Discussion Forum and Quiz of the student’s test be A, B, C,
and D and let P be passing possibility of the student.
Therefore, 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
1 1 0 0 0
1 1 0 1 1
1 1 1 0 1
1 1 1 1 1

3DATA REPRESENTATION
The expression of the following table will be
AB’CD + ABC’D + ABCD’ + ABCD
After minimizing the above equation we get,
A [D (B’C + BC’) + BC]
Circuit diagram for the above equation is
Figure 1: Circuit Diagram

4DATA REPRESENTATION
Bibliography
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Transactions on Computers, 63(8), 1895-1901.
Kempthorne, D., & Steele, A. (2014). An evaluation of different delivery methods for teaching
binary, hex and decimal conversion. Journal of Applied Computing and Information
Technology, 18(2), 2014.
Mano, M. M. (2017). Digital logic and computer design. Pearson Education India.
Roy, S., & Setua, S. K. (2016). Arithmetic of 5th Generation Computer.
Smolka, G. (2014). Boolean Logic.
Zhang, T., Cheng, Y., Guo, J. Z., Xu, J. Y., & Liu, X. J. (2015). Acoustic logic gates and
Boolean operation based on self-collimating acoustic beams. Applied Physics
Letters, 106(11), 113503.