fcm - may intake - resend

8/7/2019 FCM - May Intake - Resend

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Section A

Answer all questions in this section

1. *When the addition of two valid 4 bit BCD results in an invalid 4 Bit BCD code, what must be

added to the result to make the code valid?

(a). 0110 (b). 0001 0000 (c). 0101 (d). 1001

2. *

(a). (5, 10, 15) (b).Not Possible (c). (14,8,13) (d).

3. *Evaluate 104

(a). 1000 (b).100 (c). 10 (d). 10,000

4. *1 104 + 3 103 + 5 102 + 7 101 + 9 100 is equivalent to?

(a). 10,000 (b).13579 (c). 9751 (d). 23

5. *The probability of the sample space is always equal to?

(a). 1 (b).1-S (c). 10 (d). 1/2

6. When rewritten without an exponent 88.99 100

is equal to?

(a). 89.89 (b). 8.899 (c). 99.88 (d). 88.99

7. Where N is the number of variables in a Boolean How many rows would a truth table representing

the following expression have (not including the row headers)? (AVB)V C V D

(a). 16 (b). 8 (c). 12 (d). 16


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8. Which of the following answers is equivalent to (A)?

(a). None (b). 0 (c). 1 (d). A

9. An event having a probability of 1 means

(a). Uncertain (b). Impossible (c). Certain (d). 50% Probable

10. *XOR 1=?

(a). X (b). 1 (c). 2 (d). X+1

Section B

Answer Ten of 15

1. *Draw a diagram to represent the following probability equation: Pr(A-B)

2. Prove the following Boolean algebra law:

3.Let U = {1,2,3,4,5,6,7,8,9,10}, S = {2,4,6,7}, and T = {x | x < 10 and x belongs to the odd counting

numbers}. Find: S' and T'

4. *Differentiate between a Subset and a Proper Subset using examples as necessary.

5. *Rewrite in expanded notation 11001100

6. *Convert the Following Number to its Binary equivalent: 999

7. *Convert and addthe following two numbers in 4 BIT BCD: 9 and 8

8. *Rewrite each number without an Exponent:

(a) 0.066 102

(b) 55.55 105

(c) 44.485 104

9. Add the following Hexadecimal numbers 67.E916 + A.BCDE16


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10. Using the laws of Boolean algebra prove that the following statements are logically equivalent:

(1) (p _ (p ^ q)) (2) p ^ q.

11. Solve for xin the following equation: 3(x 2) x= 5x 4(2 x)

12. Given the following Venn diagram, shade in ~[(B U C) A]

13. Write out the truth table for the proposition (A^B)^C

14.

15. *Name the two sets and explain briefly the difference between them, mentioning the terms

Proper Subset and Subset in your answer.

3

4

5

7

8

9

1 2

A

B

3

4

5

7

8

9

1 2

A

B


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Section C

Answer any two (2) questions from the four (4) questions listed in this section

Algorithms, Pseudo codes and Flowcharts

1a. Write an algorithm for a program which requests a 10 numbers from a user then sorts them

in order of largest to smallest.

1b. Draw a flow chart to represent the solution to the problem stated in question 1a of Section C

(above).

1c. Why is the writing of pseudocode a vital part of solving computer related problems?

Sets and Relations

2a. *Draw a venn diagram to represent the following scenario: 100 people seated at different tables

in a Mexican restaurant were asked if their party had ordered any of the following items:

margaritas, chili con queso, or quesadillas

y 23 people had ordered none of these items.

y 11 people had ordered all three of these items.

y 29 people had ordered chili con queso or quesadillas but did not order margaritas.

y 41 people had ordered quesadillas.

y 46 people had ordered at least two of these items.

y 13 people had ordered margaritas and quesadillas but had not ordered chili con queso.

y 26 people had ordered margaritas and chili con que

2b. Let a card be selected at random from an ordinary pack of 52 cards. Let A= {the card is a

spade} and B = {the card is a face card}. What is P(A), P(B) and P(A B)?

2c. Let a pair of dice be tossed. If the sum is 6, find the probability that one of the dice is 2.

Boolean Algebra and Logic Gates

3a. Draw a Truth Table for the following Expression(P _ R) ^ (Q _ R):

3b. Simplify the expression [A (A v B)] v B Using K Maps the Laws of Boolean Algebra

3c. Prove the following rule: (A ^ B) ^ C = A ^ (B ^ C)


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Vectors and Matrices

4a. Explain with examples the following terms: Vector, Matrices

4b. Give the answer to the following:

4c. ?

Detail the process of adding the 3x3 Matrix above and show the result as part of your answer.

4 3

7 2

9 0

2 5

1 6


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Vectors and Matrices

Diagram


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2. B not possible

3. 104

= 10x10x10x10 = 10000

4. 13579

Section B

5. 11001100 = 1 107

+ 1 106

+ 0 105

+ 0 104

+ 1 103

+ 1 102

+ 0 101

+ 0 100

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