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1. Complete the following table, converting from Decimal, to Binary and Hex and needed.
(6 points)
Decimal Binary Hex
15 00001111 F
51 00110011 33
43 00101011 2B
165 10100101 A5
2. Convert 5,237 into Binary Encoded Decimal (BED) ( 2 point)
Answer:
Step 1: converting each digit to 4 digit binary number.
5= 0101
2= 0010
3= 0011
7= 0111
Step 2: combining these vales
BCD: 0101001000110111
3. Complete the following table of Infix, Prefix and Postfix notation. (8 points)
Prefix Infix Postfix
*AB A*B AB*
* (-a b ) (* a d) (a-b)*(a*d) (a b -) ( a d *) *
- - 2x 7y 5 2x-7y-5 2x 7y 5 - -
+ 2x - * x 7 * 2 d 2x+((x*7)-(2*d)) X 7 * 2 d * - 2x +
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)
Answer: the numeral 2 for 7253 for base 20 is: I2D
5. Create the Truth Table for the following( 6 points):
~A ^ B
A B A^B ~(A^B)
0 0 0 1
0 1 0 1
1 0 0 1
1 1 1 0

A V B ^ ~C
A B C ~C AVB AVB^~C
T 0 0 0 1 0 0
T 0 0 1 0 0 0
T 0 1 0 1 1 1
T 0 1 1 0 1 0
F 1 0 0 1 1 1
F 1 0 1 0 1 0
F 1 1 0 1 1 1
F 1 1 1 0 1 0
Write the statement for the shaded area in the following Venn Diagrams (8 points):
6. :_______
((A ^ C) – (A^B^C)) U( (B ^ C) – (A^B^C))
7. : (AUB) – (A^B)

8. : (AUBUC) – ((A^B) – (A^C) – (B^C) + 2(A^B^C))
9. : ((A^B) + (A^C) + (B^C) - 2(A^B^C))

10. Given the following circuits, create the expression.(3 points)
ANSWER:
Expression: (A’ U B) ^ (B U ( C ^ D’))
11. Given the following circuits, create the expression and the Truth Table:
(4 points)

ANSWER:
Expression: (A^B) ^ C’
A B C C’ A^B (A^B) ^ C’
0 0 0 1 0 0
0 0 1 0 0 0
0 1 0 1 0 0
0 1 1 0 0 0
1 0 0 1 0 0
1 0 1 0 0 0
1 1 0 1 1 1
1 1 1 0 1 0
Expression: (A ^ B) ^ (C U D)

A B C D A ^ B C U D (A ^ B) ^ (C
U D)
0 0 0 0 0 0 0
0 0 0 1 0 1 0
0 0 1 0 0 1 0
0 0 1 1 0 1 0
0 1 0 0 0 0 0
0 1 0 1 0 1 0
0 1 1 0 0 1 0
0 1 1 1 0 1 0
1 0 0 0 0 0 0
1 0 0 1 0 1 0
1 0 1 0 0 1 0
1 0 1 1 0 1 0
1 1 0 0 1 0 0
1 1 0 1 1 1 1
1 1 1 0 1 1 1
1 1 1 1 1 1 1
12. In the following table, find the appropriate 8 bit ASCII code and add the correct Odd parity bit as
needed. (3 points)
ANSWER:
Character (not
HEX!!)
VALUE IN HEX 8 bit ASCII Parity Bit

A 41 01000001 0
F 46 01000110 1
f 66 01100110 0
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)
Answer: let the set be ‘A’
{ A E R | A >= -4 and A <= 19}
All Integers between zero and 54 (1 point)
Answer: let the set be ‘B’
{ B E Z | B >= 0 AND B< = 54}
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)
ANSWER:
Let G = {1, 2, 4, 6, 7, 9}
Since B= {2, 4, 6} and D= {1, 7, 9}
 G = (B U D)
16. Show set T that is the Intersection of set C and D ( 1 point)
ANSWER:
Let ‘T’ be a set with elements = {1, 7, 9}
And it is given that C= {0,1,5,7,9} and D= {1,7,9}
 T = (C ^ D)
17. List the proper subsets of set C ( 1 point)
ANSWER: since C= {0,1,5,7,9}, thus some of its proper subsets are:
a. {0}
b. {1}
c. {5}
d. {7}
e. {9}
f. {0,1}
g. {0,1,5}
h. {1,5}
i. {0,5}
j. {5,7,9}
k. {7,9}

l. {0,7}
m. {0,9}
n. {1,7}
o. {1,9}
p. {5,7}
q. {5,9}
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)
Answer: it is given that
C= {0, 1, 5, 7, 9}
D= {1, 7, 9}
 K = {0,1,2,3,5,7} is a set such that K is a subset of C and a subset of D, but not a proper
subset of D