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digital_calculations.pdf

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EE 110 Spring 2018
Homework 02
D. Willie
Homework is due, Wed Jan 31 in class. 25% credit off before midnight (scan and email). After
midnight no credit! 7 problems, 100 points total
Write your name, the assignment name, and the date at the top of the first page of each assignment.
Staple multiple pages together. Number all problems and put them in order in your assignment.
Please write clearly and draw a box around numerical answers. You will not get credit if your work is
difficult to follow or the answer in a box is not easily seen. You will not get full credit if these
directions aren?t followed.
Chapter 1 and 2 Problems from Book (Nelson, Digital Logic, Circuit Analysis, and Design), pages
75-76. Be sure to use subscripts to indicate which numbering system your answer is in.
1)
2)
3)
4)
5)
6)
7)
(10 pts total, 2.5 pts per part) Assume all of the following are negative integers except for 0.
Convert each of the following to 8-bit unsigned format numbers, then find the 1s complement and
the 2s complement of each of the following to make them negative (Nelson 1.8 and 1.9):
a) 110 10112
b) 10 10102
c) 02
d) 1000 00002
(20 pts total, 2.5 pts per answer) Calculate A, A-B, -A and ?A-B for each of the pairs of
numbers assuming a 2s complement numbering system and 8-bits. Assume A and B are initially
positive. (Nelson 1.10):
a) A=101 01012 and B=10102
b) A=110 10112 and B=010 10102
(20 pts total, 4 pts per answer) Perform the following Hexadecimal calculations (Dueck 7.11):
a) 27H ?
b) A55H ?
c) 1FFFH ?
d) F86H – 614H
e) 5D33H -7D30H (use 16s complement)
(10 pts total) Encode the following in ASCII code. Put the final answer in Hexadecimal (Nelson 1.14)
Lumberjacks
(15 pts total, 2.5 pts per answer) Convert the following to true binary, BCD and excess-3 codes
(Dueck 7.13)
a) 70910
b) 188910
(10 pts total, 2.5 pts per answer) (20 pts) Using Boolean Algebra, simplify each expression:
¯ (? ?)
a) ?? ?(? ?) ?
¯¯¯¯¯¯¯¯¯¯¯¯¯¯
¯
¯
b) ? * ?? (? ? ?¯ ?¯ * ?¯ * ?¯ ?)
c) (? ??)(? ?¯?)(? ?)
¯¯¯¯ ??
¯¯¯¯??
d) ???? ????
(15 pts, 7.5 pts per part) Using Boolean Algebra Simplify (Nelson 2.1 and 2.2):
a) ?(?, ?, ?) = ??(? ??) (? ?)(?? ??)
b)
?(?, ?, ?, ?) = ??? ?? ??? ?? ???

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