# 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