normal binary arithmetic and Boolean tables

Instructions: You may lose points for not following instructions so please read carefully. Typeyour 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
Question One
a
[½ point] How does Boolean relate to binary?
Your answer here.
b [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?
c
Your answer here.
Question two
a.
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
i.
ii.
Add the number 156 to the number 527
Subtract the number 178 from the number 1,282
a.
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
i.
ii.
b.
Subtract the number 178 from the number 1,282
Subtract the number 5271 from the number 156
Develop the full Boolean tables for the following expressions:
i. (A and B) or (C and D)
ii. (not A or not B) and not (C or B)
iii. (A or not B) and (not C or D) and not (A or D)
iv.
Question two
Binary arithmetic
a. 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
i.
Add the number 156 to the number 527
ii.
Subtract the number 178 from the number 1,282
b.
i.
ii.
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
Subtract the number 1781 from the number 1,28
Subtract the number 5271 from the number 156
c. Develop the full Boolean tables for the following expressions:
i.
(A and B) or (C and D)
ii.
(not A or not B) and not (C or B)
iii.
(A or not B) and (not C or D) and not (A or D)