w9 Sfe3013 Digital Sv

7/28/2019 w9 Sfe3013 Digital Sv

1/37

SFE3013BASIC ELECTRONICS


2/37

- DIGITAL ELECTRONICS NUMERATION SYSTEMS

(Numbers and Coding Systems)


3/37

DIGITAL ELECTRONICS

CHAPTER OUTLINE

1. Analog and Digital Signals

3. Logic Gates

4. Combining Logic gates

2. Numbers and Coding Systems

5. Simplifying Logic gates

6. Flip-Flops


4/37

1. Differentiate between analog and digital

signals.

2. Convert numbers between the numbersystems.


5/37

Numerical Presentation

The quantities that are to be measured,monitored, recorded, processed and

controlled are analog and digital,

depending on the type of system used.

There are basically two ways of

representing the numerical value ofquantities: analog and digital.


6/37

Digital circuits are electric circuits based on anumber ofdiscrete voltage levels.

Digital circuits are the most common physical

representation ofBoolean algebra and are thebasis of all digital computers.

To most engineers, the terms "digital circuit","digital system" and "logic" are interchange-able in the context of digital circuits.

1. Analog and Digital Signals


7/37

Most digital circuits use two voltagelevels labeled "Low"(0) and "High"(1).

Computers, electronic clocks, andprogrammable logic controllers (used

to control industrial processes) are

constructed of digital circuits.


8/37

Advantages

signals represented digitally can be transmittedwithout degradation due to noise.

For example, a continuous audio signal,

transmitted as a sequence of 1s and 0s, can bereconstructed without error provided the noisepicked up in transmission is not enough toprevent identification of the 1s and 0s.

An hour of music can be stored on a compactdisc as about 6 billion binary digits.


9/37


10/37

In an analog system, additional resolution

requires fundamental improvements in thelinearity and noise characteristics of eachstep of the signal chain.

In an analog system, noise from aging andwear degrade the information stored.

In a digital system, as long as the total noiseis below a certain level, the information canbe recovered perfectly.


11/37

ANALOG vs DIGITAL

In analog representation a quantity isrepresented by a voltage, current, ormeter movement that is proportional tothe value of that quantity

--> CONTINUOS VALUE

In digital representation the quantitiesare represented not by proportionalquantities but by symbols called digits.--> 0 or 1 --> DISCRETE VALUE


12/37

ANALOG DIGITAL


13/37

In digital circuits, a logic level is one of a finite

number of states that a signal can have.

Logic levels are usually represented by the

voltage difference between the signal and

ground.

The range of voltage levels that represents eachstate depends on the logic family being used.

The two levels are logical high and logical low,

which generally correspond to a binary 1 and 0respectively.


14/37

Technology L voltage H voltage Notes

CMOS 0V to VCC/2 VCC/2 to VCCVCC = supply

voltage

TTL 0V to 0.8V 2V to VCC VCC = 5V 10%

ECL VEE to 1.4V 1.2V to 0V

VEE is about

5.2V;VCC=Ground

Examples of binary logic levels:


15/37

2. NUMBERS and CODING SYSTEMS

A number system is a code that uses

symbols to refer to a number of items.

Decimal, binary, hexadecimal (HEX),

octal, binary coded decimal (BCD),

Gray code, ASCII code.


16/37

2. NUMBERS and CODING SYSTEMS

TheDecimal system is a base-ten system0,1,2,3,4,5,6,7,8,9.

The binary system is a base-two system.0 and 1

The octal system is a base-eight system.0,1,2,3,4,5,6,7.


17/37

The Hexadecimal system is a base-sixteensystem. 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F.

The position of a digit indicates its weight, or valuewithin the number.

The weights are based on powers of .. 10 in a decimal number (10 )

2 in a binary number (2 )

8 in a octal number (8 ) 16 in a Hex number (16 )

Where n is a digit position. n = -2, -1, 0, 1, 2,

..

n

n

n

n


18/37

Decimal System Weight


19/37

Binary System weight

The position of each digit (bit) in a

binary number can be assigned a

weight

1 0 1 1 1 0 1.

22 21 20 2-1 2-2 2-3


20/37

OCTAL and HEX


21/37

Octal Binary

0 000

1 001

2 010

3 011

4 100

5 101

6 110

7 111

Binary is also easily converted to the octal

numeral system, since octal uses a radix of 8


22/37

Example: Converting from

(a) octal to binary

658 = 110 101217

8= 001 111

2

(b) binary to octal:

1011002 = 101 1002 grouped = 54810011

2= 010 011

2grouped with padding = 23

8

(c) octal to decimal:

658 = (6 81) + (5 80) = (6 8) + (5 1) = 5310

1278

= (1 82) + (2 81) + (7 80) = (1 64) + (2

8) + (7 1) = 8710


23/37

decimal to binary conversion

A systematic method of converting whole numbers fromdecimal to binary is the repeated division-by-2 process.


24/37

BINARY TO DECIMAL CONVERSION


25/37

Conversion Code - Chart

DECIMAL 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

HEX 0 1 2 3 4 5 6 7 8 9 A B C D E F

BINARY 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111

http://easycalculation.com/hex-converter.php


26/37

Question 1:


27/37

Question 1:

Counting practice: count from zero to thirty-one in binary, octal,

and hexadecimal:


28/37

Convert decimal 54 to binary number

54 /2 = 27 Remainder = 0

27 /2 = 13 Remainder = 1

13 /2 = 6 Remainder = 1

6 /2 = 3 Remainder = 0



ANSWER: 5410 = 1101102


29/37


30/37

BINARY TO HEXADECIMAL CONVERSION

Convert 10110111.12

to hexadecimal

Solution:

Group the bits in four's, from the binary point

left, and from the binary point right, adding

zeros as necessary to make complete 4-bit

groups.

Answer: 10110111.12 = B7.816


31/37

HEXADECIMAL TO BINARY CONVERSION

Convert C316

to binary number

Solution:

Each HEX digit is converted to its 4-bit binary

equivalent.

C16 = 11002 316 = 00112

Answer: C316 = 110000112


32/37

Exercise 4

Convert the number1128 DECIMAL to HEXADECIMAL

Ans: 46816

Convert octal 32 to binary

Convert octal 53.7 to binary

Ans: 011010


33/37

Binary Addition

The four basic rules for adding binary digits (bits)

are as follows:

0 + 0 = 0 Sum of 0 with a carry of 0




[Excercise] Add 1111 and 1100.

Ans: 11011


34/37


35/37

The ASCII (pronounced ask-E) code assigns binary

patterns forNumbers 0 to 9

All the letters of English alphabet, uppercase and

lowercase

Many control codes and punctuation marks

The ASCII system uses 7 bits to represent each code

Hex Symbol Hex Symbol

5A Z 7A z

59 Y 79 y

... ... ... 44 D 64 d

43 C 63 c

42 B 62 b

41 A 61 a

ASCII CODE


36/37

HOMEWORK

Perform hex subtraction:

59F 2B8


37/37

THE END

Documents

w9 Sfe3013 Digital Sv