Basic ElectronicsNinth Edition

Basic ElectronicsNinth Edition

©2002 The McGraw-Hill Companies

GrobSchultz

GrobSchultz

Basic ElectronicsNinth Edition

Basic ElectronicsNinth Edition

©2003 The McGraw-Hill Companies

31CHAPTER

Digital Electronics

Topics Covered in Chapter 31

Binary and Decimal Numbers

Decimal to Binary Conversion

Hexadecimal Numbers

Binary Coded Decimal System

The ASCII Code

Logic Gates, Symbols, and Truth Tables

Boolean Algebra

DeMorgan's Theorem

Treating Unused Inputs

TTL and CMOS Circuits

Active HIGH/Active LOW Terminology

Topics Covered in Chapter 31(continued)

Topics Covered in Chapter 31(continued)

Combinational Logic Circuits

Binary Adders

Flip-Flops, Counters, and Registers

New Logic Symbols

Troubleshooting Digital Circuits

Number Systems• Decimal

Base 10; digits are 0 through 9 Most commonly used by humans

• Binary Base 2; digits are 0 and 1 Most commonly used by computers

• Hexadecimal Base 16; digits are 0 through F

• BCD Binary Coded Decimal

Decimal Binary Hex

0 0 0

1 1 1

2 10 2

3 11 3

4 100 4

5 101 5

6 110 6

7 111 7

8 1000 8

9 1001 9

10 1010 A

11 1011 B

12 1100 C

13 1101 D

14 1110 E

15 1111 F

Decimal (base 10)13410 = 4 x1 + 3x10 + 1x100 = 13410

Different Base Numbers

Binary (base 2)100001102 = 0x1 + 1x2 + 1x4

+0x8 + 0x16 + 0x32+0x64 + 1 x 128 = 13410

Hex (base 16)8616 = 6x1 + 8x16 = 13410

Logic Gates

• AND gate• OR gate• XOR gate

• NAND gate• NOR gate• XNOR gate

Inverter

(NOT gate)

Logic Inverter

• A logic inverter switches the state of its input. Changes 0 to 1

Changes 1 to 0

• Logic inverters can invert the outputs of other logic gates. Change an AND gate to a NAND gate Change an OR gate to a NOR gate Change an XOR gate to an XNOR gate

A10

B01AB

AND/NAND Logic Functions

• AND function

• NAND function

B0011

C0101

A0001

B0011

C0101

A1110

ABC

ABC

OR/NOR Logic Functions

OR function

NOR function

B0011

C0101

A0111

B0011

C0101

A1000

ABC

ABC

XOR/XNOR Logic Functions

XOR function

XNOR function

B0011

C0101

A0110

B0011

C0101

A1001

ABC

ABC

A = B+C

A = B+C

DeMorgan’s Theorems

XAB

XAB

A + B = A • B

=

A • B = A + B

AB

XAB = X

Combinational Logic Circuits

A B C X

0 0 0 0

0 0 1 0

0 1 0 0

0 1 1 0

1 0 0 0

1 0 1 1

1 1 0 1

1 1 1 1

A

BC

X

X = A(B + C)

X = ABC + ABC + ABC + ABC

A B C X

0 0 0 0

0 0 1 1

0 1 0 0

0 1 1 0

1 0 0 0

1 0 1 1

1 1 0 1

1 1 1 1

Truth Table Boolean Expression Simplify

X = BC(A + A) + AB(C + C)

X = BC + AB

Factor:

1

{

1{

Flip-Flop Circuits

• Flip-flop circuits are digital devices that hold a 0 or 1 output until some event triggers them to the opposite output.

• They are commonly used for storing digital data on a temporary basis.

Major Types of Flip-Flop Circuits

• Set/reset (SR) flip-flops.

Q

Q

S

R

Q

Q

D

CLK

Q

Q

J

K

• J-K flip flops.

• D-type flip-flops.

Q

QS

R

SR Flip-Flop with Active HIGH Inputs

Q

Q

S

R

Time

Q

Q

S

R

Q

QR

S

SR Flip-Flop with Active LOW Inputs

Q

Q

S

R

Time

+VCC

+VCC

Q

Q

S

R

Q

R

CLK

S

Time

Clocked SR Flip-Flop

Q

Q

S

RCLK

Q

Q

D

Negative-Edge Triggered D Flip-Flop

Q

CLK

D

Time

CLK

Q

Q

J

Negative-Edge Triggered JK Flip-Flop

Q

CLK

J

Time

CLKK

K

Mode J K Q

Inhibit 0 0 Q

Set 1 0 1

Reset 0 1 0

Toggle 1 1 Q

Q

Q

JCLK

K

Binary Counter

1

1

Q

Q

J

K

1

1

Q

Q

J

K

1

1

Q

Q

J

K

1

1

Q0 Q1 Q2 Q3

Q2

CLK

Q0

Q1

Q3