HW2-sol - EE2301 S2010 INTRODUCTIONTODIGITALSYSTEMSDESIGN...

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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 = ab + ac + a + bc = ab + a + c + bc = a + b + c + b = 1 (b) ab + abc + bc = abc + abc + a bc + bc = abc + bc + bc = abc + b = b (c) z( x + y)( xy + z) = ( zx + zy)( xy + z) = zxy + zxy + zx + zy = zx + zy (d) wx ( y + z) + wx (y + z )( y + z) = x ( y + z)( w + w(y + z )) = x ( y + z)( w + y + z ) = x ( yw + zw + yz + yz) = x ( yw + yz + yz) = xyw + x y z + xyz (e) ACD + AC + BCD + ACD + A BC + ABC = AD + AC + BCD + ABC = AD + 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 + CD )(A + BD + E)( A + C) = (A + BD + BE + CDE )( A + C) = ABD + ABE + ACDE + AC + BCD + BCE = ABD + ABE + AC DE + AC (b)Convert the following expression into POS form by factoring: AC + ABD + ABE + ACDE = AC + A ( BD + BE + CDE ) = (AC + A )(A + CDE + BD + BE) = A + C A + CDE + 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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HW2-sol - EE2301 S2010 INTRODUCTIONTODIGITALSYSTEMSDESIGN...

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