How to convert binary, hex, decimal using 16 bit and 2′ s

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How to convert binary, hex, decimal using 16 bit and 2′ s? and Develop the full Boolean tables?

Instructions:

You may lose points for not following instructions so please read carefully. Type your answers in a word processor and hand in a printed copy (please associate question number with each answer). For the problem solving question do this by hand on a plain sheet of paper (show all work!). Add a separate cover sheet with the assignment number and your name. Be concise and complete with all answers.

 

Discussion questions:[1½ points] – give full paragraph (4-5 sentence) answers each

 

  • [½ point] How does Boolean relate to binary?

 

Your answer here.

 

 

  • [½ point] Why does a computer uses only two values and not more than that (i.e. 10 like humans or even 3 for yes, no, maybe).

 

Your answer here.

 

 

  • [½ point] What is the purpose of 2’s compliment?

 

Your answer here.

 

 

 

 

Problem solving:[1½ points] – binary arithmetic

 

  • [½ point] For this you will use normal binary arithmetic. Please use 16 bit representations (i.e. add the leading 0’s) for each and be sure you do (and show your work) in binary not decimal
    1. Add the number 156 to the number 527

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  1. Subtract the number 178 from the number 1,282

 

 

 

 

 

 

 

 

 

 

 

 

 

  • [½ point] For this we will use 2’s compliment arithmetic. Please use 16 bit representations (i.e. add the leading 0’s) for each and be sure you do (and show your work) in binary not decimal
    1. Subtract the number 178[1] from the number 1,282

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  1. Subtract the number 5271 from the number 156

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  • [½ point] Develop the full Boolean tables for the following expressions:
    1. (A and B) or (C and D)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  1. (not A or not B) and not (C or B)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  1. (A or not B) and (not C or D) and not (A or D)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

[1] Hint: remember that this number has to be converted to 2’s complement

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