NAND & NOR Implementation - Digital Logic Design (EEE 241)

1 nand & NOR ImplementationBy : Ali MustafaNAND and NOR Implementations nand & NOR gates are universal gates. Digital circuit are frequently constructed with nand or NOR gates rather than AND andOR gates. nand and NOR gates are easier to fabricate with electronic components and are the basic gates used in all IC Digital Logic families.(covering AND,OR,NOT)DeMorgan sLawRecall the DeMorgan sLaw:(a + b) = a b (a b) = a + b a + b = (a b ) (a b) = (a + b ) ====Universal Gate NANDI will demonstrate The basic function of the nand gate. How a nand gate can be used to replace an ANDgate, an ORgate, or an INVERTER gate. How a Logic circuit implemented with AOIlogic gates can be re-implemented using only nand gates. That using a single gate type, in this case nand , will reduce the number of integrated circuits (IC) required to implement a Logic LogicNAND LogicMore ICs = More $$Less ICs = Less $$ nand Gate5 XYZ001011101110 XYY X YXZ nand Gate as an Inverter Gate6XZ0110 XXZ XXX (Before Bubble)

2 Equivalent to InverterNAND Gate as an AND Gate7 XYZ000010100111 XYY X Y XZ YXNAND GateInverterEquivalent to AND GateNAND Gate as an OR Gate8 XYZ000011101111 Equivalent to OR GateXYYXY X Y XZ XNAND GateInvertersYNANDGate Equivalent to AOIG ates9 INVERTERORANDP rocess for nand starting from a Logic expression, implement the Design with AOI the AOI Implementation , identify and replace every AND,OR, and INVERTER gate with its nand the and eliminate any double inversions ( , back-to-back inverters). the final Implementation11 Example: Design a nand Logic Circuit that is equivalent to the AOI circuit shown C B nand Implementation12 Solution Step 2 Identify and replace every AND,OR, and INVERTER gate with its nand Implementation13 Redraw the Step 3 nand Implementation14 Identify and eliminate any double Step 4 nand Implementation15 Solution Step 5 Redraw the of Equivalence16CC BC AC A C BZC AC BZCA C B AOI vs.

3 NAND17 ICTypeGatesGate / IC# ICs74LS0416174LS0824174LS32141 TotalNumber of ICs 3 ICTypeGatesGate / IC# ICs74LS00441 TotalNumber of ICs 1 Summary - nand UniversalityInverterAAAND gateABABABA + BOR gateABA + BNOR gateSelf Task Implement the following Boolean express using only nand gatesY = ABC + ABC + A BCY = AB + CDE + FY = (0,1,5)Universal Gate NORNow I will The basic function of the NORgate. How an NORgate can be using to replace an ANDgate, an ORgate or an INVERTER gate. How a Logic circuit implemented with AOIlogic gates could be re-implemented using only NORgates That using a single gate type, in this case NOR, will reduce the number of integrated circuits (IC) required to implement a Logic LogicNOR LogicMore ICs = More $$Less ICs = Less $$20 NOR GateXYZ001010100110 XYY X Y XZ 21 NOR Gate as an Inverter GateXZ0110 XXZ XXX (Before Bubble)

4 Equivalent to Inverter22 NOR Gate as an OR GateXYZ000011101111 XYYX Y XZ Y X NOR Gate Inverter Equivalent to OR Gate23 NOR Gate as an AND GateXYZ000010100111 Equivalent to AND GateXYY XY X Y XZ XNOR Gate Inverters Y24 NORGate Equivalent of AOIG atesINVERTERORAND25 Process for NOR starting from a Logic expression, implement the Design with AOI the AOI Implementation , identify and replace every AND,OR, and INVERTER gate with its NOR the and eliminate any double inversions. ( back-to-back inverters) the final ImplementationExample: Design a NOR Logic Circuit that is equivalent to the AOI circuit shown C B 27 NOR ImplementationSolution Step 2 Identify and replace every AND,OR, and INVERTER gate with its nand ImplementationRedraw Step 329 NOR ImplementationIdentify and eliminate any double Step 430 NOR ImplementationSolution Step 5 Redraw of EquivalenceBCA C AC A C A C BZC A C B CCAC BC BCB C A C B 32 AOI vs NORICTypeGatesGate / IC# ICs74LS0416174LS0824174LS32141 TotalNumber of ICs 3 ICTypeGatesGate / IC# ICs74LS02742 TotalNumber of ICs 233 Summary NOR -UniversalityInverterAAOR gateABA + BABABAND gateABNAND gateSelf Task Implement the following Boolean express using only NOR gatesY = (A +B+C)(A + B)DY = (0,1,2,4,6)

5 Conversion to nand Implementation Minimized expressions are AND-OR combinations Two illustrations for nand gates AND-invert Invert-OR Key observation: two bubbles eliminate each other Two bubbles equal straight wire How to generate a sum of mintermsusing nand ? Use AND-invert for minterms Use invert-OR for sumConversion to nand Implementation nand Example Function F = (1,2,3,4,5,7)Minimize and implement with NANDS olutionDraw K-Map 1stImplementationMultilevel nand circuits Multilevel circuits conversion all AND gates to nand with AND-invert all OR gates to nand with invert-OR all bubbles in diagram. For every bubble that is not compensated by another bubble, insert inverter. ExampleSelf Task Simplify the equation by simple gates & NANDF=(AB +A B)(C+D )Self Task Implement the following Boolean express using only nand gatesY = ABC + ABC + A BCY = AB + CDE + FY = (0,1,5) Logic Operation with NOR gate NOR can also replace NOT, AND, OR Two representations of NOR: OR-invert and invert-ANDC onverting to NOR Implementations Same rules as for nand implementationsSelf Task Implement the following Boolean express using only NOR gatesY = (A +B+C)(A + B)DY = (0,1,2,4,6)Ex-OR/NOR functionX-ORX-NOREx-OR implementations In fig.

6 (b), the first nand gate performs the operation (xy) = (x + y ).xy + x y= x yOdd function Boolean expression of three-variable of the XOR:A B C = (AB + A B)C + (AB + A B )C= AB C + A BC + ABC + A B C = (1, 2, 4, 7)Odd and Even functions The 3-input odd function is implemented by means of 2-input exclusive-OR B C = (AB + A B)C + (AB + A B )CApplications of Ex-OR/NOR Comparator Binary to Gray code convertor Adder & Subtractorcircuits Parity generator And etc.