Computer Science Fundamentals: Number Systems, Logic, and Set Theory

This assignment covers several fundamental concepts in computer science. It includes converting between decimal, binary, and hexadecimal number systems, along with converting numbers to Binary Encoded Decimal (BED). The assignment also explores prefix, infix, and postfix notations, truth tables, and set theory operations such as union, intersection, and subsets. Additionally, the assignment requires the student to analyze and represent logic circuits using expressions and truth tables. Furthermore, it involves working with 8-bit ASCII codes and parity bits, and converting hexadecimal numbers to floating-point binary representations. The assignment concludes with set builder notation and questions related to set operations.

1. Complete the following table, converting from Decimal, to Binary and Hex and needed.
(6 points)
Decimal Binary Hex
15
51
00101011
10100101
2. Convert 5,237 into Binary Encoded Decimal (BED) ( 2 point)
3. Complete the following table of Infix, Prefix and Postfix notation. (8 points)
Prefix Infix Postfix
*AB
(a-b)*(a*d)
2x-7y-5
2x+((x*7)-(2*d))
4. If there are 7,253 students but that number is in in Base 20, How many students does the
numeral 2 represent? (2 points)
5. Create the Truth Table for the following( 6 points):
~A ^ B
T
T
F
F
A V B ^ ~C
T
T
T
T
F
F
F

F
Write the statement for the shaded area in the following Venn Diagrams (8 points):
6. :_______
7. :_________

8. :_________
9. :_________

10. Given the following circuits, create the expression.(3 points) Expression:
11. Given the following circuits, create the expression and the Truth Table:
(4 points)
Expression:
T
T
T
T
F
F
F

F
Expresion:
T
T
T
T
T
T
T
T
F
F
F
F
F
F
F

F
12. In the following table, find the appropriate 8 bit ASCII code and add the correct Odd parity bit as
needed. (3 points)
Character (not HEX!!) 8 bit ASCII Parity Bit
A
F
f
Binary Decimal fraction value Power of 2
.1 ½ .5 -1
.01 ¼ .25 -2
.001 1/8 .125 -3
.0001 1/16 .0625 -4
.00001 1/32 .03125 -5

.000001 1/64 .015625 -6
13. Using the above table for reference, Convert the following Hex numbers into the appropriate
floating point representation in single precision binary. Label the three sections of the resulting
binary stream. ( 10 points)
HEX
95.6
14. Using Set Builder Notation show the sets for the following:
All Real numbers between -4 and 19 (1 point)
All Integers between zero and 54 (1 point)

(GO TO THE NEXT PAGE)

Answer the following questions based on these sets:
A={3,4,5}
B={2,4,6}
C={0,1,5,7,9}
D={1,7,9}
15. Show set G that is the Union of set B and D ( 1 point)
16. Show set T that is the Intersection of set C and D ( 1 point)
17. List the proper subsets of set C ( 1 point)
18. Create set K such that K is a subset of C and a subset of D, but not a proper subset of D(1 point)