Logic Gates Short notes | Digital Circuits - Electronics and Communication Engineering (ECE) PDF Download

 Page 1


Logic Gates
Logic gates are the fundamen tal building blo c ks of digital circuits, p erforming basic logical op erations
on binary inputs to pro duce a binary output. They are essen tial comp onen ts in the design of digital
systems, suc h as computers, micro con trollers, and comm unication devices.
1. In t ro d uction to Logic Gates
Logic gates implemen t Bo olean algebra op erations, pro cessing binary signals (0 and 1) to execute func-
tions lik e AND, OR, and NOT. Eac h gate has one or more inputs and a single output, and they are
com bined to create complex digital circuits for computation, con trol, and data pro cessing.
2. T yp es of Logic Gates
The primary logic gates and their op erations are:
• AND Gate : Outputs 1 only if all inputs are 1. Bo olean expression: Y =A·B .
• OR Gate : Outputs 1 if at least one input is 1. Bo olean e xpression: Y =A+B .
• NOT Gate : In v erts the input (0 to 1, or 1 to 0). Bo olean expression: Y =A .
• NAND Gate : Outputs 0 only if all inputs are 1 (NOT of AND). Bo olean expression: Y =A·B .
• NOR Gate : Outputs 1 only if all inputs are 0 (NOT of OR). Bo olean expression: Y =A+B .
• X OR Gate : Outputs 1 if the inputs differ. Bo olean expression: Y =A?B =A·B+A·B .
• XNOR Gate : Outputs 1 if the inputs are the same. Bo olean expression: Y =A?B =A·B+A·B .
3. T ruth T ables
Eac h logic gate’s b eha vior is describ ed b y a truth table, summarizing the output for all p ossible input
com binations. F or a t w o-input gate:
• AND: Y =1 only when A =B =1 .
• OR: Y =1 when A =1 , B =1 , or b oth.
• X OR: Y =1 when A ?=B .
• NAND, NOR, XNOR: Complemen t of AND, OR, X OR outputs, resp ectiv ely .
F or NOT ( single input): Y =1 when A =0 , and Y =0 when A =1 .
4. Univ ersal Gates
NAND and NOR gates are univ ersal gates, meaning an y logic function can b e implemen ted using only
NAND or only N OR gates. F or example:
• NOT: A = NAND(A,A) .
• AND: A·B = NAND( NAND(A,B), NAND(A,B)) .
• OR: A+B = NAND( NAND(A,A), NAND(B,B)) .
This prop ert y sim plifies circuit design and man ufacturing.
1
Page 2


Logic Gates
Logic gates are the fundamen tal building blo c ks of digital circuits, p erforming basic logical op erations
on binary inputs to pro duce a binary output. They are essen tial comp onen ts in the design of digital
systems, suc h as computers, micro con trollers, and comm unication devices.
1. In t ro d uction to Logic Gates
Logic gates implemen t Bo olean algebra op erations, pro cessing binary signals (0 and 1) to execute func-
tions lik e AND, OR, and NOT. Eac h gate has one or more inputs and a single output, and they are
com bined to create complex digital circuits for computation, con trol, and data pro cessing.
2. T yp es of Logic Gates
The primary logic gates and their op erations are:
• AND Gate : Outputs 1 only if all inputs are 1. Bo olean expression: Y =A·B .
• OR Gate : Outputs 1 if at least one input is 1. Bo olean e xpression: Y =A+B .
• NOT Gate : In v erts the input (0 to 1, or 1 to 0). Bo olean expression: Y =A .
• NAND Gate : Outputs 0 only if all inputs are 1 (NOT of AND). Bo olean expression: Y =A·B .
• NOR Gate : Outputs 1 only if all inputs are 0 (NOT of OR). Bo olean expression: Y =A+B .
• X OR Gate : Outputs 1 if the inputs differ. Bo olean expression: Y =A?B =A·B+A·B .
• XNOR Gate : Outputs 1 if the inputs are the same. Bo olean expression: Y =A?B =A·B+A·B .
3. T ruth T ables
Eac h logic gate’s b eha vior is describ ed b y a truth table, summarizing the output for all p ossible input
com binations. F or a t w o-input gate:
• AND: Y =1 only when A =B =1 .
• OR: Y =1 when A =1 , B =1 , or b oth.
• X OR: Y =1 when A ?=B .
• NAND, NOR, XNOR: Complemen t of AND, OR, X OR outputs, resp ectiv ely .
F or NOT ( single input): Y =1 when A =0 , and Y =0 when A =1 .
4. Univ ersal Gates
NAND and NOR gates are univ ersal gates, meaning an y logic function can b e implemen ted using only
NAND or only N OR gates. F or example:
• NOT: A = NAND(A,A) .
• AND: A·B = NAND( NAND(A,B), NAND(A,B)) .
• OR: A+B = NAND( NAND(A,A), NAND(B,B)) .
This prop ert y sim plifies circuit design and man ufacturing.
1
5. Logic Gate Implemen tation
Logic gates are implemen ted using semiconductor devices:
• CMOS T ec hnology : Uses complemen tary pairs of n-MOSFET s and p-MOSFET s for lo w p o w er
consumption and high noise imm unit y .
• TTL (T ransistor-T ransistor Logic) : Uses BJT s for faster switc hing but higher p o w er consump-
tion.
F or example, a CMOS NAND gate uses t w o n-MOSFET s in series and t w o p-MOSFET s in parallel,
con trolled b y the input signals.
6. Applications of Logic Gates
Logic gates are used in:
• Com binational Circuits : A dders, m ultiplexers, and deco ders.
• Sequen tial Circuits : Flip-flops, registers, and coun ters.
• Micropro cessors : F or arithmetic, logic, and con trol op erations.
• Memory Devices : In RAM, R OM, and flash memory .
• Comm unication Systems : F or signal enco ding and deco ding.
7. Practical Considerations
• Propagation Dela y : The time tak en for a gate’s output to resp ond to input c hanges, affecting
circuit sp eed.
• F an-in/F an-out : F an-in is the n um b er of inputs a gate can handle; fan-out is the n um b er of gates
it can driv e. Both are limited b y tec hnology .
• P o w er Consumption : CMOS gates consume less p o w er than TTL, critical for p ortable devices.
• Noise Margin : T he abilit y to tolerate noise without affecting output, higher in CMOS.
• T emp erature Effects : Gate p erformance ma y v ary with temp erature, requiring robust design.
8. Logic Gate F amilies
Logic gates are group ed in to families based on implemen tation tec hnology:
• CMOS : Lo w p o w er, high noise imm unit y , used in mo dern ICs.
• TTL : F ast but p o w er-h ungry , used in older systems.
• ECL (Emitter-Coupled Logic) : V ery high sp eed for sp e cialized applications.
Eac h family has sp ecific v oltage lev els for logic 0 and 1, affecting compatibilit y .
9. Conclusion
Logic gates are the cornerstone of digital electronics, enabling the implemen tation of complex logical
functions through simple binary op erations. Their v ersatilit y , com bined with adv ancemen ts in CMOS
tec hnology , has driv en the dev elopmen t of mo dern digital systems. Understanding gate op erations,
c haracteristics, and practical limitations is essen tial for designing e?icien t and reliable digital circuits.
2