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Unformatted text preview: ECE2022 Homework 2 D07 Name :
ECE Box Number:
Each problem is worth the number of points shown. Clearly Show the ﬁnal answer to each problem by drawing a heavy square around it. Show your work in a neat, organized and easily followed sequence if you expect to get any partial credit.
This assignment is due Thursday, March 29, bring to class to hand in. Problem 1  10 points total a) Simplify the following Boolean expression by applying the properties of Boolean algebra, until
it matches the simpliﬁed form given. Use the rule numbers, law and theorem names given on the
attached sheet to indicate which transformations you have applied in each step of the process. Since
the answer is given, you will be graded on properly expressing the equations at each step in the
seqence as well as the name of property used at that step. Note, in the follow I have used the prime notation, x’ as used in the textbook, to denote the not
operation and shown as T in class. a) Show that xy + X’y + Z’y’ +y’z can be simpliﬁed to 1. b) Show that ab’+a’b+a’b’+b’+bc+b’c can be simpliﬁed to a’+b’+c. Problem 2  20 points total a) Write the Boolean expression for F that most directly can be obtained (that is, don’t attempt
any form of simpliﬁcation) from the logic circuit below: X b) Form the truth table that fully describes the operation of this circuit and enter the values in the
table provided below. Truth Table
X Y Z F
0 0 0 —
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1 c) From the truth table above form the Standard (Canonical) SOP expression for this logic function: F: d) From the truth table above form the Standard (Canonical) POS expression for this logic function: Problem 3  20 points total a (Spts) State the function F implemented by this circuit as a Boolean expression. (There are many forms and simpliﬁcations for F. Just write down the one that most directly expresses the function
of this circuit). F 2 b (10pts) State the Standard (Canonical) SOP form for this function here:
F :: c (5pts) The function of this circuit could have been implemented as a 2 level logic circuit instead of as it is now, a 3 level circuit. Show a 2 level solution, using a circuit diagram like that above,
using only NAND gates. Problem 4  20 points total
For the logical function, F, described by the following truth table: (a) Three Variable Map X Y Z F
O 0 0 0
0 0 1 0
0 1 0 1
0 1 1 1
1 0 O O
1 0 1 1
1 1 0 0
1 1 1 1 a) State the Standard (Canonical) SOP Boolean logic expression formed by its minterms. b) State the SOP solution you ﬁnd above in decimal format by completing the statement below: 1“— EX’ylz 0) State the Standard (Canonical) POS Boolean logic expression formed by its maxterms. d) State the POS solution you ﬁnd above in decimal format by completing the statement below: F(X,Y,Z) : ngyyz ...
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 Spring '07
 Cyganski

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