Boolean Algebra and Number Systems

 Assignment Details

Assignment Description

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
   • 1111010What 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.