Boolean Algebra and Number Systems

by

 Assignment Details

Assignment Description

Complete the following in a paper of 12 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 twos 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 twos 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.