Mathematics

Complete the following in a paper of 1–2 pages:

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

5. 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

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

· 4469736372657465204D617468656D617469637320697320434F4F4C21

7. 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.

· 00010001

· 01011100

· 1111010

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

8. 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

· 0

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

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

· 9A88

· 4AF6

· DA

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

Complete the following in a paper of 1

2 pages:

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 Ë q’) V

( r V q)] Ë s

4.

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

5.

Prove or disprove that the following 2 expressions are equivalent. Use either the related laws for

your proof, or complete the two truth tables:

o

(A + C)(AD + AD’) +

AC + C

o

A + C

6.

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

7.

Convert each of the following signed binar

y 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.

8.

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

.

9.

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

work.

o

9A88

o

4AF6

Complete the following in a paper of 1–2 pages:

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

5. Prove or disprove that the following 2 expressions are equivalent. Use either the related laws for

your proof, or complete the two truth tables:

o (A + C)(AD + AD’) + AC + C

o A + C

6. 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

7. 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.

8. 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.

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

work.

o 9A88

o 4AF6

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