Applications of Discrete Mathematics and Statistics-Questions

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.

1. 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.

1. 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.