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# Lecture 3

## 1.

Digital system courseIlyassov Baurzhan, PhD, associate professor,

department of intellectual system and cybersecurity.

## 2.

Announcement !!!Labs works will be offline at Friday every week.

- For IT-2003 and IT-2004 at 8:30 a.m. at C2-240K

- For IT-2001 and IT-2002 at 10:40 a.m. at C1-348K

Do not miss labs!!!

## 3.

Homework1. Reading – Chapter 3 of the course book: Digital Electronics:

Principles and Applications 8th Edition by Roger Tokheim, pages 4383

2. Answer to the Chapter Review Questions at the end of the chapter

3, page 83-86.

3. Review Labs 3

Next week it will be the test based on Lecture 3.

## 4.

rd3

Lecture: Logic Gates

This lecture will help you to:

1) Memorize the name, symbol, truth table, function, and Boolean expression for

the seven basic logic gates (AND, OR, NOT, NAND, NOR, XOR, XNOR).

2) Draw a logic diagram of any of the seven basic logic functions using only NAND

gates.

3) Sketch logic diagrams illustrating how two-input gates could be used to create

gates with more inputs.

4) Convert one type of basic gate to any other logic function by using inverters.

5) Identify pin numbers and manufacturer's markings on both TTL and CMOS DIP

package ICs.

6) Recognize new logic gate symbols used in dependency notation (IEEE standard

91-1984).

7) Analyze the operation of several simple logic gate applications.

## 5.

Logic gatesThe logic gate is the basic building block of any digital circuit.

The logic gates are the building blocks for even the most complex computers.

The term "logic" is usually used to refer to a decision-making process. A logic gate, then, is

a circuit that can decide to say yes or no at the output based upon the inputs.

Logic gates can be constructed by using…

Simple switches, relays, vacuum tubes,

transistors and diodes

integrated circuit

## 6.

Logic gatesThe task performed by a logic gate is called its logic function.

Logic functions can be implemented by

hardware (logic gates)

by programming devices such as

microcontrollers or computers.

## 7.

The AND gateThe AND gate is sometimes called the "all or nothing gate."

the AND gate circuit says yes (light on) at the output

only when we have a yes (switches closed) at both

inputs.

AND circuit using switches.

AND gate logic symbol.

## 8.

The AND gateInputs

Outputs

Y

A

B

Switch

Voltage

Binary

Switch

Voltage

Binary

Light

Binary

LOW

0

LOW

0

No

0

LOW

0

HIGH

1

No

0

HIGH

1

LOW

0

No

0

HIGH

1

HIGH

1

Yes

1

AND truth table.

The truth table for the AND gate gives all the possible input combinations of A and B

and the resulting outputs. Thus the truth table defines the exact operation of the AND

gate. This truth table is said to describe the AND function.

The unique output from the AND gate is a HIGH only when all inputs are HIGH.

## 9.

Boolean expression"input A is ANDed with input B to get

output Y."

The short method used to represent this statement is called its

Boolean expression ("Boolean" from Boolean algebra-the

algebra of logic)

The multiplication dot (∙) is used to symbolize the

AND function in Boolean expressions.

In common practice Boolean expression A ∙ B = Y

can be simplified to AB = Y.

Both A ∙ B = Y or AB = Y describe the two-input

AND function.

## 10.

AND gateSummary

The term logic function implies

the logical relationship between

inputs and output

while

logic gate suggests the physical

implementation.

We might say that an AND logic

gate (IC) performs the AND

function.

The unique output of the AND

function is a HIGH output only

when all inputs are HIGH.

## 11.

The OR gateThe OR gate is sometimes called the "any or all gate."

Inputs

This OR truth table is said to describe the

inclusive OR function.

The unique output from the OR gate is a LOW

only when all inputs are LOW.

Y

A

B

OR circuit using switches.

Outputs

Switch

Binary

Switch

Binary

Light

Binary

Open

0

Open

0

No

0

Open

0

Closed

1

Yes

1

Closed

1

Open

0

Yes

1

Closed

1

Closed

1

Yes

1

OR truth table.

## 12.

The OR gateOR logic gate symbol

“Inputs A and B are being ORed to produce an

output Y.”

Boolean expression.

the plus (+) sign is the Boolean symbol for OR.

## 13.

AND gateSummary

The unique output of the OR

function is a LOW output only when

all inputs are LOW.

## 14.

The inverter (Not circuit)the inverter complements or inverts the input.

The NOT circuit is often called an inverter.

The job of the NOT circuit (inverter) is to give an

output that is not the same as the input.

A logic symbol

Inputs

Outputs

A

Y

Voltages

Binary

LOW

0

HIGH

1

HIGH

1

LOW

0

the overbar (-) symbol above the output shows that A has

been inverted or complemented. We say ‘not A’.

Voltages Binary

Inverter truth table.

Boolean expression for an inverter

The apostrophe symbol shows that A has been

inverted or complemented

## 15.

The inverter (Not circuit)When a signal passes through an inverter, it can be

said that the input is inverted or complemented.

We can also say it is negated.

Alternative inverter logic symbol

(note bubble at input).

Effect of double inverting.

## 16.

Noninverting buffer/driver.Noninverting buffer/driver logic symbol.

It serves no logical purpose (it does not invert),

but is used to supply greater drive current at its

output than is normal for a regular gate.

Buffer/drivers are available in both noninverting

and inverting form.

Logic symbol for three-state buffer

## 17.

The NAND GateThe AND, OR, and NOT gates are the three

basic circuits that make up all digital circuits.

Invert bubble (small circle)

on the right end of the

symbol means to invert the

output of AND.

NAND gate logic symbol.

Truth table for AND and NAND

Output

Inputs

B

A

AND

NAND

0

0

0

1

0

1

0

1

1

0

0

1

1

1

1

0

The NAND gate is a NOT AND, or an inverted

AND function.

## 18.

NAND GateSummary

The unique output of the NAND function is a LOW

output only when all inputs are HIGH.

## 19.

Truth table for OR and NORThe NOR GATE

The NOR gate is actually a NOT OR gate.

The output of an OR gate is inverted to form a NOR

gate.

NOR gate logic symbol.

Output

Inputs

B

A

OR

NOR

0

0

0

1

0

1

1

0

1

0

1

0

1

1

1

0

## 20.

NOR Gate SummaryThe unique output from the NOR gate is a HIGH

only when all inputs are LOW.

## 21.

The Exclusive OR Gate (XOR gate)The exclusive OR gate is sometimes referred to as the "odd but not even gate."

The term "exclusive OR gate" is often shortened to "XOR gate"

Truth table for OR and XOR

Output

Inputs

XOR gate logic symbol

Boolean expression

B

A

OR

XOR

0

0

0

0

0

1

1

1

1

0

1

1

1

1

1

0

## 22.

The Exclusive OR Gate (XOR gate)The unique characteristic of the XOR gate is

that it produces a HIGH output only when an

odd number of HIGH inputs are present.

Three-input XOR gate symbol

Output

Inputs

C

B

A

Y

0

0

0

0

0

0

1

1

0

1

0

1

1

0

0

1

0

1

1

0

1

0

1

0

1

1

0

0

1

1

1

1

## 23.

XOR Gate SummaryThe unique output of the XOR gate is a HIGH only when an odd number of inputs

are HIGH.

## 24.

The Exclusive NOR Gate (XNOR gate)The term "exclusive NOR gate" is often shortened to "XNOR gate."

Truth table for XOR and XNOR

Output

Inputs

XNOR gate logic symbol.

Boolean expression

B

A

XOR

XNOR

0

0

0

1

0

1

1

0

1

0

1

0

1

1

0

1

The unique output of the XNOR gate is a LOW only when an

odd number of inputs are HIGH which is the opposite from the

XOR gate.

## 25.

3 inputs-XNOR gateThe unique output of the XNOR gate is a

LOW only when an odd number of inputs

are HIGH.

Three-input XNOR gate symbol

Inputs

Output

Output

C

B

A

XOR

XNOR

0

0

0

0

1

0

0

1

1

0

0

1

0

1

0

1

0

0

1

0

0

1

1

0

1

1

0

1

0

1

1

1

0

0

1

1

1

1

1

0

## 26.

XNOR Gate SummaryThe unique output of the XNOR gate is a

LOW only when an odd number of inputs

are HIGH which is the opposite from the

XOR gate.

## 27.

The NANO Gate as a Universal GateWe have learned about the seven types of gating circuits and now

know the characteristics of the AND, OR, NAND, NOR, XOR, and XNOR

gates and the inverter.

The NAND gates can be used to make other types of gates.

We will be using the NAND gate as a "universal gate."

## 28.

The NANO Gate as a Universal Gate## 29.

## 30.

Gates with More Than Two Inputs?

Three-input AND gate.