Applications of Discrete Mathematics and Statistics in Information Technology HW Please see attached

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:  

4. Complete the truth table of the following Boolean expression:

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.