HW2-sol - EE2301 S2010 HOMEWORK#2(20pts DueFeb.16,2010...

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Unformatted text preview: EE2301 S2010 INTRODUCTIONTODIGITALSYSTEMSDESIGN HOMEWORK#2(20pts) DueFeb.16,2010 Grade Problems 3, 5(b), 7(e), 8(a) and 11 - 4pts each 1.Simplifyusingalgebraicmanipulations: (a) a’ ( b’ + c) + a + bc’ = a’b’ + a’c + a + bc′ = a’b’ + a + c + bc′ = a + b’ + c + b = 1 (b) ab + a’bc’ + bc = abc + abc ′ + a ′ bc ′ + bc = abc + bc ′ + bc = abc + b = b (c) z( x’ + y)( x’y + z) = ( zx’ + zy)( x’y + z) = zx’y + zx’y + zx’ + zy = zx’ + zy (d) w’x’ ( y’ + z) + wx’ (y + z’ )( y’ + z) = x’ ( y’ + z)( w’ + w(y + z’ )) = x’ ( y’ + z)( w’ + y + z’ ) = x’ ( y’w’ + zw’ + y’z′ + yz) = x’ ( y’w’ + y’z′ + yz) = x’y’w’ + x ′ y′ z ′ + x′yz (e) A’C’D’ + AC’ + BCD + A’CD’ + A’ BC + AB’C’ = A’D’ + AC’ + BCD + A’BC = A’D’ + AC’ + BCD 2. (a)Convert the following expression into SOP form by multiplying out: (A + B + C’ )(A + B + D)(A + B + E)(A + D’ + E)( A’ + C) = (A + B + C’D )(A + BD’ + E)( A’ + C) = (A + BD’ + BE + C’DE )( A’ + C) = A’BD′ + A’BE + A’C′DE + AC + BCD’ + BCE = A’BD′ + A’BE + A′C′ DE + AC (b)Convert the following expression into POS form by factoring: AC + A’BD’ + A’BE + A’C’DE = AC + A’ ( BD’ + BE + C’DE ) = (AC + A’ )(A + C’DE + BD’ + BE) = A’ + C ¡¢ A + C’DE + B D ′ + E ¡£ = A’ + C ¡ A + B + C ′ DE ¡ A + C ′ DE + D ′ + E ′ ¡ = A’ + C ¡ A + B + C ′ ¡ A+ B + D ¡ A+ B + E ¡ (A + D ′ + E) 3.Problem3.32 Z = ABC + DE + ACF + AD ′ + AB ′ E ′ = A BC + CF + D ′ + B ′ E ′ ¡ + DE = A + DE ¡ DE+ BC + CF + D...
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This note was uploaded on 06/04/2010 for the course EE 2301 taught by Professor Larrykinney during the Spring '09 term at Minnesota.

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HW2-sol - EE2301 S2010 HOMEWORK#2(20pts DueFeb.16,2010...

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