EE 5900 Advanced EE 5900 Advanced Algorithms for Robust Algorithms for Robust VLSI CAD S!ring "009VLSI CAD S!ring "009Combinational CircuitsCombinational Circuits#vervie$#vervie$Combinational CircuitCombinational CircuitChip Design stylesChip Design stylesFull-custom designFull-custom designCell library based designCell library based designProgrammable Logic ArrayProgrammable Logic ArrayAug 11, 2015 PF- 2Combinational LogicAug 11, 2015 PF- !Combinational LogicCombinational CircuitsCombinational CircuitsA combinational circuit consists o" logic A combinational circuit consists o" logic gates #hose outputs, at gates #hose outputs, at any timeany time, are , are determined by combining the $alues o" determined by combining the $alues o" the inputs%the inputs%For For nn input $ariables, there are 2input $ariables, there are 2n n possible binary input combinations%possible binary input combinations%For each binary combination o" the For each binary combination o" the input $ariables, there is one possible input $ariables, there is one possible output%output%Aug 11, 2015 PF- &Combinational LogicCombinational Circuits %cont&'Combinational Circuits %cont&''ence, a combinational circuit can be 'ence, a combinational circuit can be described by(described by(1% 1%A truth table that lists the output $alues "or A truth table that lists the output $alues "or each combination o" the input $ariables, oreach combination o" the input $ariables, or2% 2%mm )oolean "unctions, one "or each output )oolean "unctions, one "or each output $ariable%$ariable%CombinationalCircuitn-inputs m-outputs ******Aug 11, 2015 PF- 5Combinational LogicCombinational $s% +e,uential CircuitsCombinational $s% +e,uential CircuitsCombinational circuits are Combinational circuits are memory-less%memory-less% -hus, the output $alue depends ./L0 on the -hus, the output $alue depends ./L0 on the current input $alues%current input $alues%+e,uential circuits consist o" combinational +e,uential circuits consist o" combinational logic as #ell as memory elements 1used to logic as #ell as memory elements 1used to store certain circuit states2% .utputs store certain circuit states2% .utputs depend on ).-' current input $alues and depend on ).-' current input $alues and pre$ious input $alues 13ept in the storage pre$ious input $alues 13ept in the storage elements2%elements2%Aug 11, 2015 PF- 4Combinational LogicCombinational $s% +e,uential CircuitsCombinational $s% +e,uential CircuitsCombinationalCircuitn-inputs m-outputs1Depend only on inputs2CombinationalCircuitn-inputs m-outputs+torage5lements/e6tstatePresentstateSe(uential CircuitCombinational CircuitAug 11, 2015 PF- 7Combinational LogicIm!ortant Design Conce!tsIm!ortant Design Conce!ts8odern digital design deals #ith $arious 8odern digital design deals #ith $arious methodsmethods and and toolstools that are used to design and that are used to design and $eri"y comple6 circuits and systems% $eri"y comple6 circuits and systems% Concepts(Concepts(Design 'ierarchyDesign 'ierarchyComputer-Aided-Design 1CAD2 toolsComputer-Aided-Design 1CAD2 tools'ard#are Description Languages 1'DLs2'ard#are Description Languages 1'DLs2Aug 11, 2015 PF- 9Combinational LogicDesign )ierarch*Design )ierarch*++Divide,and,Con(uer-Divide,and,Con(uer- approach used to approach used to cope #ith the challenges o" designing cope #ith the challenges o" designing comple6 circuits and systems 1many times comple6 circuits and systems 1many times in the order o" millions o" gates2%in the order o" millions o" gates2%Circuit is bro3en into Circuit is bro3en into bloc.sbloc.s, repetiti$ely%, repetiti$ely%Aug 11, 2015 PF- :Combinational LogicDesign )ierarch* Design )ierarch* E/am!le0 9,in!ut odd function %for counting 1 of 2 in in!uts'E/am!le0 9,in!ut odd function %for counting 1 of 2 in in!uts'Aug 11, 2015 PF- 10Combinational Logic3h* is )ierarch* useful43h* is )ierarch* useful4;educes the comple6ity re,uired to ;educes the comple6ity re,uired to design and represent the o$erall design and represent the o$erall schematic o" the circuit%schematic o" the circuit%;euse;euse o" bloc3s is possible%