This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: ECE 270 Introduction to Digital System Design Fall 2011 TakeHomaWork for Module 2 — Due September 14, 2011 1. [10 points] Given the truth table, below, determine the following: Y Z F XaYaz) (a) [6 points] F(X,Y,Z) expressed as: mm
mm
unm m“ an onset.‘ 2X,y,l(0,1,5,7) an“ n a“ an offset: TCx,y,z(2,3,4,6)
_l (b) [4 points] Truth tables for the dual FD and complement F' functions: Y Z F'(X,Y,Z) I!
I!
ME
I!
E mumm
an
Eli‘
n
um
I!
a“
_ 2. [10 points] Given the truth table, below, determine F(X,Y,Z) expressed as: X Y Z F(X,Y,Z .
 a canonical sum—of—products: X'Y’Z' + X’Y'Z + X’YZ + XY'Z + XYZ'  a canonical product—ofsums: (X+Y'+Z)(X’+Y+Z)(X’+Y’+Z’) ECE 270 Introduction to Digital System Design Fall 2011 3. [20 points] Practice ﬁnding dual and complement functions/circuit realizations. Draw
an ANDOR circuit realization of each, and write sum—of—products expressions for the
dual and complement functions. (a) [4 points] F(X,Y,Z) = X(Y’+Z) + X'Y (AND0R circuit only) = XY' + XZ + X’oY (b) [8 points] G(X,Y,Z) = FD(X,Y,Z) the DUAL of function F, above, plus AND0R circuit = (X+Y') 0 (X+Z) 0 (X’+Y) = XY + XYZ +X’0Y’0Z (C) [8 points] H(X,Y,Z) = F'(X,Y,Z) the COMPLEMENT of function F plus AND0R circuit = (X’+Y)  (X’+Z’)  (X+Y’) = X'Y' + X'Y’Z' +XY0Z’ ECE 270 Introduction to Digital System Design Fall 2011 TakeHomaWork for Module 2 — Due September 16, 2011 1. [20 points] For the circuit shown below, derive the following formal descriptions:
(a) [4 points] truth table
(b) [4 points] ON set
(c) [4 points] OFF set
((1) [8 points] sumof—products expression "1' X ‘f + x 52" ~s~ e ON set: 2 W,x,y,z (3,4,6,7,11,12,14,15) OFF set: TC w,x,y,z (0,1,2,5,8,9,10,13) SOP expression: X’Y + X'Z' + Y°Z ECE 270 Introduction to Digital System Design Fall 2011 2. [20 points] Practice drawing and labeling 3, 4, and 5variab1e Kmaps. Number each square with
the corresponding miniterrn number, and write the expression for each miniterm in its corresponding square. 2Variable Kmap example: X! I X
0 2
Y' I X’Y' I XY'I 1 3
Y X'Y XY (a) [2 points] 3Variable Kmap: F(X,Y,Z) (b) [8 points] 4Variab1e Kmap: F(W,X,Y,Z) 5 1 3 9
W'X Y’Z W X Y'Z W X’Y‘Z X 1 WX'Y’Z 3 7 15 11
X’YZ W'XYZ WXYZ WX'YZ w' 5Variab1e map is drawn as two 4variab1e maps, Visualized as being “stacked” in 3space ECE 270 Introduction to Digital System Design Fall 2011 TakeHomaWork for Module 2 — Due September 19, 2011 1. [10 points] For the function mapped below: (a) [5 points]Write a minimal sumof—products expression and calculate its cost:
/' l I ‘ l  1 I “a.
(x : X z? +« w *H + w E + We C of” T S / 5/ try”: [1 7L g cit—i (M :1? HM) (b) [5 points] Write a minimal productof—sums expression and calculate its cost:
/‘ I I ~
I’ 1‘ Y 7? 4w wx a, WW {537" 5' i; 6" (it? it: i f" “F L/ ‘33th a; If." / Fall 201 l ECE 270 Introduction to Digital System Design 2. [10 points] Express the complement of the following function as an ON SET and draw
a NAND—NAND circuit realization: F(X,Y,Z) = Y’ + M 3. [10 points] Express the dual of the following function as an OFF SET and draw a
NOR—NOR circuit realization: F(X,Y,Z) = Y + xz' W. 3:; I? E V 1 {Ag
6‘1“: w'ﬁ ljjeééﬂﬁgwgglu: ﬁg ,OFRSE r" a? g g; g I W 4.5”? “X kg) f3‘” w; l‘ 1JLuU—u‘yswpmwunu.w,w4r"‘ Fall 2011 ECE 270 Introduction to Digital System Design 4. [30 points] Assuming that only true variables are available, realize the function
F(X,Y,Z) mapped below three different ways:
(a) [10 points] Using only 7400 (quad 2input NAND) chips
(b) [10 points] Using only 7402 (quad 2input NOR) chips
(0) [10 points] Using only 7403 (quad 2input opendrain NAND) chips (1: 747%” Show complete schematics for each realization, along with your derivations. ( (1 ECE 270 Introduction to Digital System Design Fall 2011
TakeHomaWork for Module 2 — Due September 21, 2011 l. [20 points] Simplify the function mapped below in terms of XOR or XNOR
operators, draw a circuit realization, and compare the cost of this “simpliﬁed”
realization with minimal SOP (NANDNAND) and PoS (NORNOR) realizations. ECE 270 Introduction to Digital System Design Fall 2011 2. [20 points] Sketch the response of the circuit, below, to the input signals provided.
Assume the input signals (A, B, C) have been in the initial states shown prior to the
beginning of the chart, and that each gate has a tpLH and tpHL of 10 ns. Identifv the
hazard (by name) if one occurs in the output (F). L NO HAZARD IN OUTPUT FOR INPUT COMBINATION GIVEN ECE 270 Introduction to Digital System Design Fall 2011 3. [20 points] Equipped only With a bucket full of 2input NAND gates (plus a
breadboard, some wires, some SPST switches, an LED, some resistors, and a battery),
you must implement the function represented by the ON SET ZX,Y,Z(1,6,7) as
efﬁciently and quickly as possible. Show all of your work, plus a comglete schematic (including the switches, resistors, LED, and however many 2input NAND gates
deemed necessary). ./ ...
View
Full
Document
This note was uploaded on 02/12/2012 for the course ECE 270 taught by Professor Staff during the Spring '08 term at Purdue.
 Spring '08
 Staff

Click to edit the document details