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Dissertation

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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

(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

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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)

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))

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’ U B) ^ (B U ( C ^ D’))

11. Given the following circuits, create the expression and the Truth Table:

(4 points)

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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)

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

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:

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:

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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}

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

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

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