Boolean logic in CMOSRepresentations of Boolean logicTruth tableBoolean algebraSlide 5Slide 6CMOS gates - NOTCMOS gates - NANDCMOS gates - NORCMOS gates - ANDCMOS gates - ORUniversity of Texas at Austin CS310 - Computer Organization Spring 2009 Don FussellBoolean logic in CMOSUniversity of Texas at Austin CS310 - Computer Organization Spring 2009 Don Fussell 2Representations of Boolean logicTruth tableBoolean equationCircuit element (gate)University of Texas at Austin CS310 - Computer Organization Spring 2009 Don Fussell 3Truth tableBrute force I/O specificationGrows exponentially with number of inputsUniversity of Texas at Austin CS310 - Computer Organization Spring 2009 Don Fussell 4Boolean algebraIdentitiesx + 0 = xx + 1 = 1x + x = xx + x’ = 1x’’ = xx * 1 = xx * 0 = 0x * x = xx * x’ = 0University of Texas at Austin CS310 - Computer Organization Spring 2009 Don Fussell 5Boolean algebraCommutativityx + y = y + xx * y = y * xAssociativityx + (y + z) = (x + y) + zx * (y * z) = (x * y) * zUniversity of Texas at Austin CS310 - Computer Organization Spring 2009 Don Fussell 6Boolean algebraDistributivex * (y + z) = x*y + x*zx + (y * z) = (x+y) * (x+z)= x + xy + xz + yz= x(1+y) + xz + yz= x + xz + yz= x(1+z) + yz= x + yzDe Morgan(x + y)' = x' * y'(x * y)' = x' + y'University of Texas at Austin CS310 - Computer Organization Spring 2009 Don Fussell 7CMOS gates - NOTgndIn Out0 11 0University of Texas at Austin CS310 - Computer Organization Spring 2009 Don Fussell 8CMOS gates - NANDgndabVddA B Out0 0 10 1 11 0 11 1 0University of Texas at Austin CS310 - Computer Organization Spring 2009 Don Fussell 9CMOS gates - NORabVddA B Out0 0 10 1 01 0 01 1 0University of Texas at Austin CS310 - Computer Organization Spring 2009 Don Fussell 10CMOS gates - ANDNO!Logically correct, butviolates n to n and p to p rule,passes weak valuesA B Out0 0 00 1 01 0 01 1 1VddABOutVddABOutUniversity of Texas at Austin CS310 - Computer Organization Spring 2009 Don Fussell 11CMOS gates - ORABOutVddA B Out0 0 00 1 11 0 11 1