Mod2_F11_Solns

# Mod2_F11_Solns - ECE 270 Introduction to Digital System...

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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 on-set.‘ 2X,y,l(0,1,5,7) an“ n a“ an off-set: 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’-Y-Z + X-Y'-Z + X-Y-Z' - a canonical product—of-sums: (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 AND-OR 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 (AND-0R circuit only) = X-Y' + X-Z + X’oY (b) [8 points] G(X,Y,Z) = FD(X,Y,Z) the DUAL of function F, above, plus AND-0R circuit = (X+Y') 0 (X+Z) 0 (X’+Y) = X-Y + X-Y-Z +X’0Y’0Z (C) [8 points] H(X,Y,Z) = F'(X,Y,Z) the COMPLEMENT of function F plus AND-0R circuit = (X’+Y) - (X’+Z’) - (X+Y’) = X'-Y' + X'-Y’-Z' +X-Y0Z’ 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] sum-of—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 5-variab1e K-maps. Number each square with the corresponding miniterrn number, and write the expression for each miniterm in its corresponding square. 2-Variable K-map example: X! I X 0 2 Y' I X’Y' I XY'I 1 3 Y X'Y XY (a) [2 points] 3-Variable K-map: F(X,Y,Z) (b) [8 points] 4-Variab1e K-map: 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' 5-Variab1e map is drawn as two 4-variab1e maps, Visualized as being “stacked” in 3-space 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 sum-of—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 product-of—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 + x-z' 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 2-input NAND) chips (b) [10 points] Using only 7402 (quad 2-input NOR) chips (0) [10 points] Using only 7403 (quad 2-input open-drain 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 (NAND-NAND) and PoS (NOR-NOR) 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 2-input 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 2-input NAND gates deemed necessary). ./ ...
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Mod2_F11_Solns - ECE 270 Introduction to Digital System...

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