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  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 )
    1. Prove or disprove that the following 2 expressions are equivalent. Use either the related laws for your proof, or complete the two truth tables:
    2. (A + C)(AD + AD’) + AC + C 
  • A + C

  1. The following is a message coded in ASCII using one byte per character and then represented in hexadecimal notation. What is the message?

    • 4469736372657465204D617468656D617469637320697320434F4F4C21
    1. 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.
    2. 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.
    2. 12
  • -2
  • -8
  • 0
  1. 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.
    2. 9A88
  • 4AF6
  • DA
  1. What is the hexadecimal sum of 9A88 and 4AF6 in hexadecimal and decimal? Show all of your work.
 
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