Satish Chandra, Assistant Professor, P P N College, Kanpur 1

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1 8/7/4 LOGIC GTES CE NPN Transistor Circuit COMINTIONL LOGIC Satish Chandra ssistant Professor Department of Physics P PN College, Kanpur circuit with an output signal that is logical function of the inputs. circuit with one or more input voltages but only one output voltage. They are of two types. asic gates NOT, OR & ND.. Combinational gates a) Universal gates NOR& NND b) rithmatic gates Ex OR & Ex NOR. Equivalent CE Circuit Transistor as a switch ZERO LRGE STURTION CUT OFF Logic Circuits SIC GTES OPEN SWITCH CLOSED SWITCH Transistor Inverter NOT Gate NOT Gate Y Y gate with only one input and one output. Output state is always opposite the input state n INVERTER. V in LOW HIGH V out HIGH LOW Y = Satish Chandra, ssistant Professor, P P N College, Kanpur

2 8/7/4 OR Gates Two input OR gate Three input OR gate CSE : is low and is low. CSE : is low and is high. CSE : is high and is low. CSE 4: is high and is high. Y Y = + Y = + + C C Y OR Gate Symbols OR Gate OR Gate Two input Three input Four input Y = + Y = + + C Y = + + C + D Two or more input signals but only one output signal. Output is high if any or all of the inputs are high. Logical Symbol OR gate performs logical addition oolean expression Y = + CSE : is low and is low. CSE : is low and is high. CSE : is high and is low. CSE 4: is high and is high. 4 5 ND Gates Two input ND Gate Three input ND Gate CSE : is low and is low. CSE : is low and is high. CSE : is high and is low. CSE 4: is high and is high. 6 Y Y =. 7 Y =..C C Y 8 Satish Chandra, ssistant Professor, P P N College, Kanpur

3 8/7/4 ND Gate Symbols ND Gate ND Gate Two input Three input Four input Y =. Y =..C Y =..C.D Two or more input signals but only one output signal. Output is high if all of the inputs are high. Logical lsymbol ND gate performs logical multiplication oolean expression Y =. CSE : is low and is low. CSE : is low and is high. CSE : is high and is low. CSE 4: is high and is high. 9 Logic Circuits OOLEN LGER oolean lgebra OR ddition Laws ND Multiplication + = Laws. = + =. = + =. = + =. = oolean lgebra Commutative Laws ssociative Laws + = + + ( + C) = ( + ) + C. =..(.C) = (.). C 4 oolean lgebra oolean lgebra Distributive Laws bsorptive Laws ( + C) =. +.C. +. = +.C = ( + ).( + C).( + ) =.( + ) = +. = + Complement Theorem = De Morgan s Theorem + =.. = + Logic Circuits UNIVERSL GTES & RITHMETIC GTES Satish Chandra, ssistant Professor, P P N College, Kanpur

4 8/7/4 NOR Gate CSE : is low and is low. CSE : is low and is high. CSE : is high and is low. CSE 4: is high and is high. NOR Gate Y Y = + NOR Gate Two or more input signals but only one output signal. Output is low if any or all of the inputs are high. Logical Symbol oolean expression Y = NOR Gate CSE : is low and is low. CSE : is low and is high. CSE : is high and is low. CSE 4: is high and is high. NOT Gate OR Gate ND Gate NOR as a Universal gate.. NND Gate CSE : is low and is low. CSE : is low and is high. CSE : is high and is low. CSE 4: is high and is high. NND Gate Y Y = NND Gate CSE : is low and is low. CSE : is low and is high. CSE : is high and is low. CSE 4: is high and is high. NND as a Universal gate.. NOT Gate OR Gate ND Gate Satish Chandra, ssistant Professor, P P N College, Kanpur 4

5 8/7/4 Ex OR Gate Ex OR Gate Ex OR Gate Y =. +. Y =. +. Y = Y Two or more input signals but only one output signal. Output is high if the inputs are different. Logical lsymbol oolean expression Y = Ex NOR Gate Ex NOR Gate Ex NOR Gate Y =. +. Y =. +. Y = Y Two or more input signals but only one output signal. Output is high if the inputs are same. Logical lsymbol oolean expression Y = PPLICTIONS PRITY CHECKER PPLICTIONS INRY TO GRY CODE CONVERTER INRY Y = for even parity Y = for odd parity 4 GRY INRY GRY 44 Logic Circuits RITHMETIC CIRCUITS 45 Satish Chandra, ssistant Professor, P P N College, Kanpur 5

6 8/7/4 HLF DDER HLF DDER FULL DDER n elementary circuit. Used to adds two binary digits at a time. It performs binary addition Consists of an XOR gate whose output gives the sum and an ND gate whose output gives the carry of addition. H CRRY SUM Carry Sum CRRY =. SUM = Used to add three binary digits at a time. It performs binary addition of two bits and a carry. Consists of two half hlfadders and an OR gate FULL DDER FULL DDER PRLLEL INRY DDER 9:8:8 PM Satish Chandra, P PN College, Kanpur 49 Input Carry F Output Carry Sum C in C out SUM 5 Used to add two binary numbers. For example 4 First column needs only a Half dder. For any other column (except First), use Full dder. 5 S S S S S 4 IT PRLLEL INRY DDER 4 IT PRLLEL INRY DDER HLF SUTRCTOR F CRRY F CRRY F CRRY H S 4 S S S S 5 F F F H 5 n elementary circuit used to subtract one binary digit from another. It performs binary subtraction handles two bits at a time and can be used for the LS column. Consists of an XOR gate whose output gives the difference and an ND gate whose output gives the borrow of subtraction. One input of ND gate inverts itself using the NOT gate. 54 Satish Chandra, ssistant Professor, P P N College, Kanpur 6

7 8/7/4 HLF SUTRCTOR FULL SUTRCTOR FULL SUTRCTOR HS ORROW DIFFERENCE orrow Difference ORROW =. DIFFERENCE = Used to subtract two binary digits with one borrow digit at a time. It performs binary subtraction of two bits and a borrow and can be used for higher order columns. Consists of two half subtractors and an OR gate input orrow FS FULL SUTRCTOR Output orrow Difference o in o out Differ 58 PRLLEL INRY SUTRCTOR Used to subtract two binary numbers. For example First column needs only a Half Subtractor. For any other column (except First), use Full Subtractor. 59 S S S S 4 IT PRLLEL INRY SUTRCTOR orrow orrow FS FS orrow FS orrow HS S S S S 6 4 IT PRLLEL INRY SUTRCTOR FS FS FS HS 6 Logic Circuits DT PROCESSING CIRCUITS 6 MULTIPLEXERS Multiplex means many into one. circuit with many inputs but only one output. y applying control signals, only one selected input can be transmitted to the output. lso called a data selector, because the output bit depends on the input data bit that is selected. 6 Satish Chandra, ssistant Professor, P P N College, Kanpur 7

8 8/7/4 MULTIPLEXERS M CONTROL SIGNL Four to one Multiplexer Y MULTIPLEXERS D N INPUT SIGNLS MULTIPLEXER OUTPUT SIGNL D D D Y = D n where n is decimal equivalent of 9:8:8 PM Satish Chandra, P PN College, Kanpur SIXTEEN to one Multiplexer Sixteen to one Multiplexer SIXTEEN to one Multiplexer 745 Strobe G C D Y Y = D n D D D D D 4 W = Dn D 5 D 6 D 7 D 8 D 9 D D D D D 4 67 D 5 9:8:8 PM Satish Chandra, College, P P N Kanpur 68 x x H x x 69 SIXTEEN to one Multiplexer 745 W = En DEMULTIPLEXERS Demultiplex means one into many. circuit with only one input and many outputs. y applying control signals, input signal can be transmitted to any one of the output lines. INPUT SIGNL DEMULTIPLEXERS M CONTROL SIGNL DEMULTIPLEXER N OUTPUT SIGNLS 7 7 9:8:8 PM Satish Chandra, P PN College, Kanpur 7 Satish Chandra, ssistant Professor, P P N College, Kanpur 8

9 8/7/4 One to four Demultiplexer DEMULTIPLEXERS One to sixteen Demultiplexer Y Y Y Y Y n = D where n is decimal equivalent of One to Sixteen Demultiplexer 7454 One to sixteen Demultiplexer DECODER Decoder is similar to demultiplexer, with one exception there is no data input. Only inputs are the control bits DECODER M CONTROL SIGNL DECODER N OUTPUT SIGNLS One to Sixteen Decoder DT and STROE inputs are grounded. The bubbles at the output shows that the output is low when it is active. One to Sixteen Decoder 9:8:8 PM Satish Chandra, P PN College, Kanpur Satish Chandra, ssistant Professor, P P N College, Kanpur 9

10 8/7/4 CD TO DECIML DECODERS CD stands for inary Coded Decimal. CD number is a four bit binary group that represents one of the ten decimal digits through 9. Example: Decimal number 496 Decimal CD TO DECIML DECODERS No CD TO DECIML DECODERS CD INVLID ENCODER ENCODER DECIML TO CD ENCODER n encoder converts non digital data to digital data. n encoder has n = m, input lines and m output lines. Only one of the input line will be active. The output lines generate a binary code corresponding to the that input line. N INPUT SIGNL ENCODER M OUTPUT SIGNL 9:8:9 PM Satish Chandra, P P N College, Kanpur 85 9:8:9 PM Satish Chandra, P PN College, Kanpur 86 9:8:9 PM Satish Chandra, P P N College, Kanpur 87 DECIML TO CD ENCODER The decimal to CD encoder with inputs and 4 outputs. The switches to 9 are push button switches like a pocket calculator. When button is pressed, the C and D OR gates have high inputs, therefore output is CD= i.e. decimal is converted into its equivalent binary number. Similarly, if you press button 5, the output will be CD= and for switch 9, we get CD= DECIML TO CD ENCODER 7447 DECIML TO CD ENCODER 7447 TRUTH TLE 9:8:9 PM Satish Chandra, P P N College, Kanpur 88 9:8:9 PM Satish Chandra, P P N College, Kanpur 89 9:8:9 PM Satish Chandra, P P N College, Kanpur 9 Satish Chandra, ssistant Professor, P P N College, Kanpur