# Expert Answers

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

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

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

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

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

o 4469736372657465204D617468656D617469637320697320434F4F4C21

6. Convert each of the following signed binary byte representations to its equivalent base-ten representation. What would each byte represent in Binary Coded Decimal? Show your work step by step.

o 00010001

o 01011100

o 1111010

What is the signed binary sum of 1011100 and 1110101 in decimal? Show all of your work.

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

o 12

o -2

o -8

o 0

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

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

o 9A88

o 4AF6

o DA

What is the hexadecimal sum of 9A88 and 4AF6 in hexadecimal and decimal? Show all of your work.

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

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

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

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

o 4469736372657465204D617468656D617469637320697320434F4F4C21

6. Convert each of the following signed binary byte representations to its equivalent base-ten representation. What would each byte represent in Binary Coded Decimal? Show your work step by step.

o 00010001

o 01011100

o 1111010

What is the signed binary sum of 1011100 and 1110101 in decimal? Show all of your work.

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

o 12

o -2

o -8

o 0

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

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

o 9A88

o 4AF6

o DA

What is the hexadecimal sum of 9A88 and 4AF6 in hexadecimal and decimal? Show all of your work.

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