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Unformatted text preview: f ) / h 5
ECE2022 HWK 3 /—\ D07
Homework is due Tuesday April 3, 2006. Problem 1 — 30 points We will design part of a set of logic circuits that tests numbers for divisbility for certain prime
numbers as part of an information encryption system. The binary number A is represented by a
four bit unsigned number: A = (a3, a2, a1, do) where (10 is the least signiﬁcant bit, etc. The circuit
you must design will have a single output, F, which must take on the value of 1 if A is divisible by 2 or 3 and zero otherwise, except when A = 0 (which is “technically” divisible by any number) for
which case we want F 2 0. (3) Give the truth table for F as a function of a3, a2, a1, a0. \4 o
0
0
o
7)
0
D
0
t
l
l
J
l
l
l
l (b) Write out the canonical sum of minterms expression for F. .—
— f0: 613474121; + 434;“.00'4‘2342‘33404 434,161,30 +9525”; 1 + GJQL4,49 +QJZquQo {Q] at 3'30 +afqzqi§0+ “ﬁzqﬂo (c) Obtain a simpliﬁed expression for F using a Karnaugh Map. (Be sure to show the Karnaugh
map and the prime implicants (rectanges) you have selected for the simpliﬁcation on your homework sheet.) Be careful, this is a tricky one, make sure you choose essential prime
implicants ﬁrst! (e) Draw the circuit diagram, that implements F. Problem 2  40 points total For each of the following truth tables, use a Karnaugh map to produce a simpliﬁed sum of products
expression. The X’s in the tables indicate “don’t cares”. Be sure to show your Karnaugh map with
clearly circled groups that correspond to your Sum of Products solution. Please draw your ﬁnal
Karnaugh maps, clearly labelled and the resulting simpliﬁed logic expressions next to them on the
next two blank sheets. (a) Three Variable Map x Y z A 0 0 0 1 Q 00 (9‘ H ‘O
0 01 0 w! 010 1 011 1 100 1 101 0 1 10 1 111 1 (c) Three Variable Map X A Y Z 01010110
00110011 00001111 Problem 3 — 30 points total For the function given;
F : (A+C)(A'+B)+B’C+BC’+BC (3) Produce a truth table that expresses F as a function of A, B, and C. _
A g c (Mo (A’+ 1:3 s'o a) no P 0 O o o I O 0 O 0
o o \ l I " 0) o l
O \ O 0. I 0 l: 0 (
o) M {“ng “Lam W 90m A...“ t
' a 0 1 0 0 0 0 C9
l 0 l l 0 l 0 0 l
I Q 0 l l 0 q 0 I
l l l l l b o \ a (b) Use a Karnaugh map to produce a simpliﬁed sum of products form. (Show both the Karnaugh
map and Sum of Product expression) A{00& &\ \\ lo (c) Draw the circuit diagram for an implementation from your simpliﬁed sum of products expression using just AND Gates and OR gates (assumming as usual ’that you have access to each literal
and its logical inversion). (d) Draw the circuit diagram of a NAND gate only implementation from your simpliﬁed sum of
products expression. ‘9‘ F’cc~
ED ’le P“; Q Dom—{joﬂrd afL Z
5&5 o 6’ 0" r (9) Use a Karnaugh map to produce a simpliﬁed product of sums form. (Show both the Karnaugh
map and simpliﬁed expression) F = (Em) (f) Draw the circuit diagram for an implementation from your simpliﬁed product of sums expression using just AND Gates and OR gates (assumming as usual that you have access to each literal
and its logical inversion). ASW’ ...
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 Spring '07
 Cyganski

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