CMOS NAND Gate Explained: Circuit, Working, Implementation, and Truth Table

Summary

In this VLSI lecture, Professor Redes Dolaqia explains the design of a CMOS NAND gate. The lecture covers the basic functionality of a NAND gate, its Boolean equation, and truth table. The professor then details how to implement the NAND gate using CMOS transistors, specifically N-type and P-type MOSFETs (nMOS and pMOS). The explanation includes the pull-up and pull-down networks, the series and parallel connections, and how the circuit operates under different input conditions. The video concludes with a functional analysis of the circuit and a request for viewer feedback.

Takeaways

• 🖥️ The video introduces the design of a CMOS NAND gate, explaining the structure and function of the gate.
• 📝 The NAND gate's Boolean equation is Y = (A ⋅ B)̅, with two inputs, A and B, where the output Y is determined by the logic.
• 🔢 The truth table for the NAND gate shows that if any input is 0, the output will be 1. Only when both inputs are 1 will the output be 0.
• 🔄 The NAND gate is implemented using CMOS transistors, specifically pMOS and nMOS transistors.
• 📶 For the NAND gate, the pull-up network is made with pMOS transistors in parallel, and the pull-down network is made with nMOS transistors in series.
• ⚙️ The basic structure of a CMOS circuit includes a VDD power supply at the top, a pull-up network (pMOS), a pull-down network (nMOS), and an output in between.
• 🔧 The operation of the NAND gate using CMOS transistors depends on the connection of pMOS and nMOS in the circuit, which changes based on the logic values of A and B.
• 📊 When A and B are 0, both pMOS transistors are on and nMOS transistors are off, resulting in a logic 1 output.
• 🧠 The video discusses how pMOS transistors are on when the gate input is 0, and nMOS transistors are on when the gate input is 1.
• 📲 The circuit behavior changes with different combinations of A and B values, explaining how the NAND gate functions through pMOS and nMOS transistor activity.

Q & A

What is the Boolean equation of a NAND gate with two inputs?

The Boolean equation of a two-input NAND gate is Y = (A · B)'. This means the output Y is the complement of the AND operation between inputs A and B.

What happens to the output of a NAND gate when any of the inputs is 0?

If any of the inputs to a NAND gate is 0, the output will always be 1.

How many possible input combinations exist for a two-input NAND gate?

For a two-input NAND gate, there are four possible input combinations: (0,0), (0,1), (1,0), and (1,1).

What is the output of a NAND gate when both inputs are 1?

When both inputs of a NAND gate are 1, the output will be 0.

How are PMOS and NMOS transistors arranged in a CMOS NAND gate?

In a CMOS NAND gate, PMOS transistors are arranged in parallel, while NMOS transistors are arranged in series.

What is the role of the pull-up and pull-down networks in a CMOS NAND gate?

The pull-up network, made of PMOS transistors, is responsible for providing a connection to the positive supply (VDD) when activated, while the pull-down network, made of NMOS transistors, connects the output to ground when activated.

What does it mean for a PMOS transistor to be 'on'?

A PMOS transistor is considered 'on' when its gate input is at logic 0, causing it to behave like a short circuit.

What is the function of an NMOS transistor when its gate is at logic 1?

When the gate of an NMOS transistor is at logic 1, the NMOS is 'on' and acts as a short circuit, allowing current to flow.

What is the output of the CMOS NAND gate when both inputs A and B are 0?

When both inputs A and B are 0, the output will be logic 1, as both PMOS transistors (Q1 and Q2) will be on, and both NMOS transistors (Q3 and Q4) will be off.

How does the CMOS NAND gate function when one input is 0 and the other is 1?

When one input is 0 and the other is 1, the output will be logic 1 because at least one PMOS transistor will be on and one NMOS transistor will be off, preventing the output from being pulled to ground.

Outlines

00:00

🔍 Introduction to CMOS NAND Gate Design

Professor Redes Dolaqia introduces the lecture by explaining the concept and function of a CMOS NAND gate. The professor first defines the NAND gate and its Boolean equation, Y = (A · B)', and illustrates its logic symbol. The professor then explains the truth table, detailing how the NAND gate produces an output of 1 when any input is 0, and describes the four possible input combinations. The paragraph concludes with an overview of how CMOS transistors (nMOS and pMOS) are arranged in series and parallel configurations to implement the NAND gate.

05:02

⚙️ CMOS Transistor Configuration for NAND Gate

The professor details how to configure pMOS and nMOS transistors in CMOS technology for a NAND gate. The pull-up network uses pMOS transistors arranged in parallel, while the pull-down network consists of nMOS transistors in series. The paragraph explains the connection process for each transistor based on the Boolean operation A · B, emphasizing the structural setup where pMOS transistors receive inputs in parallel and nMOS transistors are connected in series. The description also covers grounding and output extraction in the circuit, ensuring the proper formation of the NAND gate using CMOS technology.

10:02

📝 Functionality of CMOS NAND Gate

The professor walks through the CMOS NAND gate circuit’s functionality using a truth table and transistor states (q1, q2 for pMOS and q3, q4 for nMOS). The paragraph explains the behavior of pMOS and nMOS transistors in various input combinations (0, 0; 0, 1; 1, 0; and 1, 1). The explanation covers how the circuit yields different outputs based on the input values, detailing how pMOS transistors turn on with a logic 0 input and nMOS transistors activate with a logic 1 input. The paragraph illustrates each scenario step by step, concluding with the output results for each case. Finally, the professor invites viewers to provide feedback for future content.

Keywords

💡CMOS

CMOS stands for Complementary Metal-Oxide-Semiconductor, a technology used to construct integrated circuits. It is essential in building logic gates like the NAND gate by using both p-type (PMOS) and n-type (NMOS) transistors. The video focuses on using CMOS technology to design a NAND gate, which is central to modern digital logic.

💡NAND Gate

A NAND gate is a fundamental digital logic gate that performs the NOT-AND operation. Its Boolean equation is Y = (A ⋅ B)'. In the video, the professor explains how a NAND gate functions and demonstrates its implementation using CMOS transistors. It's crucial to understanding the gate's behavior and how it affects digital circuits.

💡Boolean Equation

A Boolean equation represents the algebraic expression for logic gate operations. For a NAND gate, the equation is Y = (A ⋅ B)'. The video uses this equation to explain the logic behind the NAND gate and how it is implemented using transistors in CMOS technology.

💡Truth Table

A truth table is a table that shows all possible input combinations and their corresponding output for a logic gate. In the video, the professor explains the truth table for the NAND gate, highlighting that the output is 1 unless both inputs are 1, in which case the output is 0.

💡PMOS Transistor

A PMOS transistor is a type of transistor in CMOS technology that turns on when its gate receives a logic 0. In the video, the PMOS transistors are used in the pull-up network of the NAND gate. They are placed in parallel for the dot operation in the CMOS NAND gate design.

💡NMOS Transistor

An NMOS transistor is a transistor that turns on when its gate receives a logic 1. In the video, NMOS transistors are used in the pull-down network of the NAND gate. They are connected in series for the dot operation in the CMOS implementation of the NAND gate.

💡Pull-Up Network

A pull-up network is the part of a CMOS circuit made of PMOS transistors. Its role is to connect the output to the high voltage (VDD) when the transistors are on. The professor in the video explains how this network functions within the NAND gate design, ensuring the correct output when certain input combinations are applied.

💡Pull-Down Network

A pull-down network consists of NMOS transistors in a CMOS circuit that connects the output to ground when activated. The video explains how the pull-down network works in tandem with the pull-up network to produce the correct output for a NAND gate.

💡Short Circuit

A short circuit refers to a state where an electrical circuit allows current to flow with little or no resistance. In the video, the professor describes how when a PMOS or NMOS transistor is 'on', it behaves like a short circuit, enabling current to flow between terminals.

💡Open Circuit

An open circuit is the opposite of a short circuit, where the circuit is incomplete, and no current flows. In the video, an 'off' PMOS or NMOS transistor creates an open circuit, preventing current from flowing, which is crucial for determining the output of the NAND gate in various input states.

Highlights

Introduction to VLSI lecture series and CMOS NAND gate design by Professor Redes Dolaqia.

Explanation of the NAND gate's Boolean equation: Y = (A . B)' and its logic symbol.

Introduction to the NAND gate truth table with two inputs (A and B) and four combinations (00, 01, 10, 11).

Explanation of the NAND gate functionality: If any input is 0, the output is 1.

Detailing the implementation of a NAND gate using CMOS transistors: nMOS and pMOS.

In NAND gate design, pMOS should be connected in parallel and nMOS in series for dot operations.

Description of the pull-up network made with pMOS transistors and the pull-down network made with nMOS transistors.

Common CMOS structure: Pull-up network with VDD, pull-down network with ground, and the output taken in between.

Designing a CMOS NAND gate circuit by connecting pMOS in parallel and nMOS in series.

Explanation of the operation of nMOS and pMOS transistors: nMOS turns on with logic 1 and pMOS with logic 0.

Simulation of the circuit's functionality for different input combinations: 00, 01, 10, and 11.

For input 00: pMOS transistors are on, nMOS transistors are off, and output is logic 1 (VDD).

For input 01: pMOS Q1 is on, Q2 is off, nMOS Q3 is off, Q4 is on, and the output is logic 1.

For input 10: pMOS Q1 is off, Q2 is on, nMOS Q3 is on, Q4 is off, and the output is logic 1.

For input 11: pMOS transistors are off, nMOS transistors are on, and the output is logic 0 (ground).

Transcripts

welcome to vlsi lecture series i

professor redes dolaqia is going to

explain you design of

cmos nand gate in this video so here

first i'll explain you what is nand gate

how it functions

after that we will implement nand gate

by using

cmos transistor so in cmos transistor we

have nmos and pmos

so by using nmos and pmos we will

implement nand gate over here

so as if we talk about nand gate then

its boolean equation

that is y if my output is y

then y is equals to if i have two inputs

a

and b then a dot b whole bar

that is my boolean equation and as if we

talk about

its symbol then

its logic symbol that is this

where with and we need to place bubble

over here so this is my output y

and here we have input a and b

there can be multiple input even but

here i have shown you

two input nand gates so we have two

inputs a and b

now let me explain you true table

so in its truth table we have two inputs

over here

a and b and my output

that is y so see

if you see the working of nand gate then

it explains

if any input is logic 0

then output is 1 so for nand gate if any

input is logic 0

then output will be 1 so with input a

and b

there are total 4 combinations 0 0

0 1 1 0 and 1 1

and if you see working if any input is 0

output is 1. so 0 0 1 here 0

1 means 0 input is there so output is 1

1 0 that is even 1 1 and 1 1 means 0

here there is no input which is 0 means

output is

1 so this is how true table is there

with

nand gate now before we implement

this nand gate by using cmos we should

know some basics

see here in nand operation

we have dot operation right

so when you perform dot operation you

see a dot b

whole bar so when you have dot operation

at a time

you should have pmos in parallel

and you should have nmos in series

so in dot operation pmos that should be

there in parallel

and nmos that should be there in series

now here one more thing that one should

know

see when you implement

any logic gate by using cmos transistor

its structure should be like this here

we should have vdd supply

and here i am just considering one block

and this block that is made up of

pull up network and pull up network

that we have it by having pmos

transistor

so here with pmos transistor we have

multiple inputs

right and after that there will be pull

down network so i am considering a block

so this is my pull

down network and pull down network that

should be made up of

nmos transistor and here i am showing

inputs to nmos transistor here we should

ground this

and output that will be coming from here

right so this is how common structure is

there

with cmos right where

after vdd there should be pull up

network and below that there will be

pull down network

and in between that there will be output

like this

right now let us try to understand how

to

implement this nand gate by using

pmos and nmos right so pull up network

that will be by pmos

and pull down network that will be by

nmos now you see

in nand gate as i have told you

it is a dot b whole bar so operation

is dot operation and in dot operation

pmos

should be there in parallel and nmos

should be there in series

right so you see here

we have vdd as per this

right after that there is pull up

network now we need to have

pmos transistor connection now see in

dot operation

pmos should be there in parallel so here

i am connecting

pmos in parallel right and

here we have operation that is a dot b

so

he here pmos is having input

a and it should be in parallel

and here we have second pmos that is

having input

b and you see

those two are in parallel over here so

this is my

pull up network now

see in pull down network there will be

nmos

and here in dot operation nmos should be

there in series

so here i am connecting nmos

in series you see

so with one nmos input is a

and with second and mos input is b and

this is what i need to ground

so this is my pull down network and here

i'll be taking output

right so this is how we can form a

circuit

of nand gate by using cmos

in cmos with upper network we will be

having pull up network and with this

we will be having pull down network

now let us try to understand how this

circuit functions

by truth table so it will be giving you

more clear idea

so here we have input

a and b and here we will be having

transistors

so here i have let us say this is q

one is q two this is q three

and this is q four so this is my q 1

q 2 and these are p mos

and here we have q 3 and q 4

and these are n

mos and here i have output

y so this is how i am going to make

a truth table and we will see how

this circuit functions right

now before i explain you how this

circuit functions

one should know how pmos and nmos

functions so let me explain you how pmos

and nmos functions

so here if i talk about nmos

then this is my nmos

where this is my gate terminal and if

you see this connection in that

here there will be drain terminal and

here there will be source terminal

now in this if my input is logic 1

means if g is equals to 1 this nmos

that will be on and if this

gate is at logic 0 we can say this nmos

that will be off and

if you talk about pmos then

you see in pmos here there will be

bubble

with gate and here

you see this terminal will be source

terminal and this terminal will be

drain terminal right so you see with

this pmos

here we have source

and here we have drain

while this with this nmos here there

will be

drain terminal and here there will be

source terminal

with this q4 this is drain and this is

source

and in this pmos if gate is equals to

logic 0 in that case

this pmos will be on and if gate is

equals to

1 in that case this pmos will be

off what is the meaning of on

on means it will be having short circuit

over here

and what will be the meaning of off

there will be open circuit over here

right now let us consider

this input and how output is coming

that we will be observing in this

circuit so if my input

is 0 0 in that case

you see a and b both are 0

so pmos that will be on

and nmos that will be off so as this

pmos

is on this q1 and q2

that will be on and this q3 and q4

that will be off

and as per that you see my output that

will be vdd

means we can say it is logic 1

right let us have second case with a

and b if a is 0 and b is 1

then you see a is connected with q1 and

q3 so q1 is pmos so if

a is 0 this pmos is on

and this q3 is nmos so it will be

off so this is on

and this is off and you see b is one

so b is one means p mos is one so q two

that will be off and

q four is having input b so b is one

so it will be on so this is q4 that is

on

and this will be off so now you see

this is on right so

here output will be vdd and this is off

so your output is vdd and

that is referred as logic one

now let us have third case so that is

one zero

so in that if you see pmos then

here see a is connected with q one

that is one so it will be off

and this b is connected with q two so

that is p motion b is zero so it will be

on

[Music]

and here q3 is connected with nmos

and here a is 1

so q3 will be

on and

this q4 that is nmos and that is having

input 0 so it will be off

so now you see again output will be vdd

as this is open circuit so

output will be vdd means logic one

now if input a and b both are one one

then you see a and b both both are

having one

input and those are pmos with

q one and q2 so that will be off

and q3 and q4 both are nmos and

input is logic 1 means both are on and

as both

are on output will be ground

means logic 0. so this is how

complete circuit functions with cmos

nand gate

i hope that you have understood this

video please do give your valuable

suggestions the reason is your

suggestions matters to me and based on

that in future

i'll be making videos which will be

resolving your queries

so please do give your valuable

suggestions thank you so much for

watching this video