Calculus and Above

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1. The following is a...

1. The following is a message in ASCII. What does it say?

010010010010000001110111011000010110111001110100001000000111010001

10111100100000011001 1101100101011101000010000001100001011011100010

000001000001001000000110100101101110001000000111010001101000011010

0101110011001000000110001101101100011000010111001101110011

2. The following is a message coded in ASCII using one byte per character and then represented in hexadecimal notation. What is the message?

4469736372657465204D617468656D617469637320697320434F4F4C21

3. Convert each of the following binary representations to its equivalent base-ten representation. Show your work step by step.

• 10001

•(NNN) NNN-NNNN

• 01011100

• 110101

4. Convert each of the following base-ten representations to its equivalent two’s complement in 7 bits. Show all of your work.

• 12

• -2

• -8

• 22

• 0

Define the highest and lowest integer that can be represented in this 7-bit two’s complement representation.

5. What bit patterns are represented by the following hexadecimal notations? Show all of your work.

• 9A88

• 4AF6

• DA

• AD

6. Simplify the following Boolean expression: AB(A + B)(C + C)

7. Design the combinatorial circuit for: (p’ *r) + q

8. Design the combinatorial circuit for: [(p Λ q’) V ( r V q)] Λ s

9. Complete the truth table of the following Boolean expression: p’ Λ (q V r )

10. Prove or disprove that the following 2 expressions are equivalent. Use either the related laws for your proof or complete the two truth tables:

• (A + C)(AD + AD’) + AC + C

• A + C

11. The cafeteria wants to provide an electronic hot dog machine. Design the machine so that it accepts 3 choices, it has a button for each choice, and a customer can select no more than 2 of the 3 choices. Design a circuit to ensure that the above conditions are satisfied.

Input

m = mustard button (1 = pushed, 0 = not pushed)

k = ketchup button (1 = pushed, 0 = not pushed)

r = relish button (1 = pushed, 0 = not pushed)

Output

Hot dog that satisfies the constrains.

010010010010000001110111011000010110111001110100001000000111010001

10111100100000011001 1101100101011101000010000001100001011011100010

000001000001001000000110100101101110001000000111010001101000011010

0101110011001000000110001101101100011000010111001101110011

2. The following is a message coded in ASCII using one byte per character and then represented in hexadecimal notation. What is the message?

4469736372657465204D617468656D617469637320697320434F4F4C21

3. Convert each of the following binary representations to its equivalent base-ten representation. Show your work step by step.

• 10001

•(NNN) NNN-NNNN

• 01011100

• 110101

4. Convert each of the following base-ten representations to its equivalent two’s complement in 7 bits. Show all of your work.

• 12

• -2

• -8

• 22

• 0

Define the highest and lowest integer that can be represented in this 7-bit two’s complement representation.

5. What bit patterns are represented by the following hexadecimal notations? Show all of your work.

• 9A88

• 4AF6

• DA

• AD

6. Simplify the following Boolean expression: AB(A + B)(C + C)

7. Design the combinatorial circuit for: (p’ *r) + q

8. Design the combinatorial circuit for: [(p Λ q’) V ( r V q)] Λ s

9. Complete the truth table of the following Boolean expression: p’ Λ (q V r )

10. Prove or disprove that the following 2 expressions are equivalent. Use either the related laws for your proof or complete the two truth tables:

• (A + C)(AD + AD’) + AC + C

• A + C

11. The cafeteria wants to provide an electronic hot dog machine. Design the machine so that it accepts 3 choices, it has a button for each choice, and a customer can select no more than 2 of the 3 choices. Design a circuit to ensure that the above conditions are satisfied.

Input

m = mustard button (1 = pushed, 0 = not pushed)

k = ketchup button (1 = pushed, 0 = not pushed)

r = relish button (1 = pushed, 0 = not pushed)

Output

Hot dog that satisfies the constrains.

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