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Unformatted text preview: ECE2022 Homework #2 Submitted by: ECE Eiox #: Date:_ Question Grade 1 2
3
4 Total: Name ECE Box ECE 2022 Homework 2 Each problem is worth the number of points show. Clearly show the ﬁnal answer to each problem by drawing a heavy square around it. Show your
work in a neat. organized and easilv Fnllnwed sequence if you expect to get any partial credit. 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 sequence as well as the name of the property used at that step. Note: in the following, I have used the prime notation, x’, as used in the textbook to denote the not operation and shown as CL“ in class. a) Show that xy’ + xy + x’(x’ + 2) can be simpliﬁed to 1. b) Show that abc’ + a’b’c + (a’+ b’ +c’)’ + a’bc + be can be simpliﬁed to ab+ a’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: b) Form the truth table that fully describes the operation of this circuit and enter the values in
the table provided below. Y
0
0
1
1
0
0
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: F: Problem 3 — 20 points total a) (5 pts) 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: b) (10 pts) State the Standard (Canonical) SOP form for this function here: F: c) (5 pts) 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. Assuming (x, y, z, X’, y’, z’) are given, the inverters
are not considered a level of logic. Show a 2 level solution, draw a circuit diagram like that above using only NAND gates.
(hint: consider SOP with involution identity) Problem 4 — 20 points total For the logic function F described by the following truth table: Three Variable Map a) State the Standard (Canonical) SOP Boolean logic expression formed by its minterms. F =
b) State the SOP solution you ﬁnd above in decimal format by completing the statement below:
F(X,Y,Z) 2 ZX,Y,Z c) State the Standard (Canonical) POS Boolean logic expression formed by its maxterms. F: d) State the POS solution you find above in the decimal format by completing the statement
below: : Hxiy‘z 2+“. ix“ nannsz n ,z. {2% axga waxwoon @3388 no? {xix n ,Azx. $30 H
E
558953 EEEBEO E ﬂick n N.x+>.x 33:2:me
AN+>V+N H N+Cw+v0 >2>u§oomm< x + > n > + x 53:32:88
I Ta X H X . N X H N + N 5:809:03 o u o . x ﬂ H # + x xik xno+x _ buquE w i
2882 :80 25% _ oEmZ W2 i 85:53 awe—com WEBB": PawwHoEoQ ﬁfxvcgc u ﬁ+>v§+kv9+xv
x n h>+xvcw+xv Nix n ﬁtmvcfxv
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 Winter '07
 Cyganski
 Logic, Boolean Algebra, Boolean function, George Boole

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