Binary Codes: Classification of Binary Codes Explained

Summary

This video delves into the realm of binary codes, explaining the fundamental concept of representing numbers, letters, and characters using ones and zeros. It categorizes binary codes into numeric and alphanumeric, highlighting ASCII for data transmission. The script explores various numeric codes like BCD, including 8421 and 5421, and touches on negative and non-weighted codes, sequential and cyclic codes, self-complementing codes, and error detection and correction capabilities. The aim is to provide a comprehensive understanding of binary codes and their classifications, with detailed explanations in upcoming videos.

Takeaways

• 😀 Binary code is a method to represent numbers, letters, or characters using groups of ones and zeros.
• 🔢 Binary codes are categorized into numeric and alphanumeric types, with numeric codes representing numbers and alphanumeric codes representing letters, numbers, and characters.
• 🔡 ASCII is a popular alphanumeric code used for data transmission between computers and I/O devices like printers and keyboards.
• 📊 Numeric codes include various types such as OBCD8421, Grey code, and XS3 code, with the 841 BCD code being the most common.
• 📐 BCD stands for Binary-Coded Decimal, where each decimal digit is encoded into a group of four binary digits.
• 🔣 Weighted codes, like 841, 2421, and 5421, follow the positional weighting principle, where the position of a bit has a specific weight contributing to the decimal equivalent.
• 🔄 Non-weighted codes, such as XS3 and Grey code, do not follow the positional weighting principle and are used for different purposes.
• 🔄 Sequential codes increment by one binary number from the previous code, making them easy to follow in sequence.
• 🔁 Cyclic codes differ from each other by only one bit position, as seen in the Grey code where successive codes have minimal changes.
• 🔄 Self-complementing codes allow for the ninth complement of a number to be found by inverting the bits of its code, as demonstrated by the XS3 code.
• 🛡️ Some binary codes have error detection and correction capabilities, such as parity and Hamming codes, which are essential in digital communication to ensure data integrity.

Q & A

What is binary code?

Binary code is a method of representing numbers, letters, or characters using groups of ones and zeros.

How are binary codes classified?

Binary codes are classified into two main categories: numeric binary codes and alphanumeric binary codes.

What is an example of an alphanumeric binary code?

ASCII is a popular example of an alphanumeric binary code, used for transmitting data between computers and IO devices like printers and keyboards.

What does BCD stand for and how does it work?

BCD stands for Binary Coded Decimal. In BCD, each decimal digit is encoded into a group of four binary digits.

What is the most common type of BCD code?

The most common type of BCD code is the 8421 BCD code.

What is a weighted code in the context of binary codes?

A weighted code is a numeric code that obeys the positional weighting principle, where each position in the number has a specific weight contributing to the decimal equivalent.

How are the weights represented in an 8421 BCD code?

In an 8421 BCD code, the weights of each bit starting from the most significant bit (MSB) are 8, 4, 2, and 1, respectively.

What is a non-weighted code?

A non-weighted code is a binary code that does not follow the positional weighting principle, such as the XS3 and Gray codes.

What is a sequential code in binary coding?

A sequential code is a binary code where each code is one binary number greater than the previous code, ensuring a consecutive sequence.

What is the difference between a positive and negative weighted code?

In a positive weighted code, all weights are positive, while in a negative weighted code, some positions have negative weights, such as in the 8-4-2-1 code.

What is a cyclic code and how does it differ from other binary codes?

A cyclic code is a binary code where successive codes differ from each other by only one bit position, unlike other codes where the difference can be more than one bit.

What is a self-complementing code and how does it work?

A self-complementing code is a binary code where the nine's complement of a decimal digit can be obtained by simply inverting the bits (replacing 1s with 0s and vice versa) of the original code.

What is the purpose of error detecting and correcting codes in binary communication?

Error detecting and correcting codes are used in digital communication to identify and fix errors that may occur during transmission due to external noise or other factors.

Can you provide an example of an error detecting code?

Parity bit is an example of an error detecting code. It is added to the usual code to help detect errors during transmission.

What is the role of Hamming code in binary communication?

Hamming code is an example of an error correcting code. It not only detects errors but also corrects them, ensuring the integrity of the transmitted data.

Outlines

00:00

🔢 Introduction to Binary Codes

This paragraph introduces the concept of binary codes, which are methods for representing numbers, letters, or characters using groups of ones and zeros. It explains that various binary codes have evolved over time and are categorized into numeric and alphanumeric types. Numeric codes represent numerical information, while alphanumeric codes like ASCII are used for transmitting data between computers and I/O devices. The paragraph also introduces different types of numeric codes such as BCD, Gray code, and XS-3, which will be discussed in more detail in upcoming videos.

05:01

📊 Exploring Weighted and Non-Weighted Binary Codes

This paragraph delves into the concept of weighted binary codes, such as BCD 8421, 2421, and 5421, where each digit position has a specific weight. It explains how these weights are used to represent decimal numbers in binary form. For example, in the 8421 BCD code, the digits are weighted 8, 4, 2, and 1, respectively. The paragraph also introduces the idea of negative weighted codes, like 8421, where some positional weights are negative. It concludes by differentiating between weighted and non-weighted codes, with examples like the XS-3 and Gray codes.

10:02

🔄 Sequential and Cyclic Binary Codes

This paragraph discusses sequential and cyclic binary codes. Sequential codes are those where each binary number is one greater than the previous one, with 8421 and XS-3 codes serving as examples. Cyclic codes are introduced next, where successive codes differ by only one bit position, with Gray code highlighted as an example. The paragraph explains that in Gray code, the difference between successive decimal numbers is represented by a single bit change, making it a cyclic code.

🔄 Self-Complementing and Error-Detecting Codes

This paragraph covers self-complementing codes and error-detecting codes. Self-complementing codes are defined by their ability to generate the ninth complement of a decimal digit by inverting the binary digits (0s to 1s and vice versa). XS-3 and 8421 codes are given as examples. The discussion then shifts to error detection and correction, highlighting the importance of error-detecting codes like parity bits in ensuring data integrity during transmission. The paragraph emphasizes the role of these codes in detecting and correcting errors caused by external noise during digital communication.

Keywords

💡Binary Code

Binary code is a system of representing numerical, textual, or other data using only two symbols: 0 (zero) and 1 (one). It is the fundamental language of computing and digital communications. In the video, binary code is the central theme, as the script discusses various types of binary codes used for representing different kinds of information, such as numbers, letters, and characters.

💡Numeric Binary Code

Numeric binary code refers to the representation of numbers using binary digits. The script explains that these codes are used to encode numeric information in a sequence of ones and zeros. An example from the script is the BCD (Binary Coded Decimal) code, where each decimal digit is encoded into a group of four binary digits.

💡Alphanumeric Binary Code

Alphanumeric binary code is a type of binary code that represents both letters and numbers. The video script mentions ASCII as a popular example of an alphanumeric code, which is used for data transmission between computers and input/output devices like printers and keyboards.

💡BCD Code

BCD stands for Binary Coded Decimal, a type of numeric binary code where each decimal digit is encoded into a group of four binary digits. The script provides an example of 841 BCD code, explaining how each decimal digit from 0 to 9 is encoded and the significance of the weights 8, 4, 2, and 1 in the code.

💡Weighted Code

Weighted code is a classification of numeric codes where each position in the binary sequence has a specific weight, contributing to the overall decimal value. The script explains that 841, 2421, and 5421 are examples of weighted codes, with the weights determining the value of the encoded number.

💡Non-Weighted Code

Non-weighted codes do not follow the positional weighting principle, meaning that the value of the encoded number is not determined by the position of the bits. The script mentions XS3 and Gray code as examples of non-weighted codes, which are used for their unique properties, such as simplicity or error minimization.

💡Sequential Code

Sequential code is a type of binary code where each code is one binary number greater than the previous one. The script illustrates this with the 8421 and XS3 codes, where adding a binary '1' to a code yields the next code in the sequence, making it easy to understand and implement in digital systems.

💡Cyclic Code

Cyclic code is characterized by the property that successive codes differ from each other by only one bit position. The script uses the Gray code as an example, where the transition between consecutive numbers involves changing only a single bit, which helps in reducing errors during transmission.

💡Self-Complementing Code

Self-complementing code is a binary code where the nine's complement of a number can be obtained by simply inverting the bits (replacing 1s with 0s and vice versa). The script explains this concept using the XS3 code, where the code for a number and its nine's complement are mirror images of each other.

💡Error Detection and Correction

The script discusses the importance of error detection and correction in digital communication. Error detecting codes, such as parity bits, can identify when an error has occurred during transmission due to noise. Error correcting codes, like Hamming codes, can not only detect but also fix certain types of errors, ensuring data integrity.

Highlights

Introduction to binary code as a method of representing numbers, letters, or characters using ones and zeros.

Binary codes have evolved over the years into various types, mainly classified into numeric and alphanumeric categories.

Numeric binary codes represent numbers in a sequence of ones and zeros, while alphanumeric codes represent letters, numbers, and characters.

ASCII is highlighted as a popular alphanumeric code used for data transmission between computers and I/O devices.

Numeric codes include types such as OBCD8421, Grey Code, and XS3, with detailed explanations to follow in subsequent videos.

Binary Coded Decimal (BCD) explained, where each decimal digit is encoded into a group of four binary digits.

841 BCD code is the most common weighted code, with positional weights of 8, 4, 2, and 1.

Weighted codes obey the positional weighting principle, with each bit position having a specific weight.

Non-weighted codes do not follow the positional weighting principle, with examples given as XS3 and Grey Code.

Sequential codes are identified by each binary number being one greater than the previous, exemplified by 8421 and XS3 codes.

Cyclic codes differ from each other by only one bit position, as demonstrated by the Grey Code.

Self-complementing codes allow for the ninth complement of a number to be obtained by inverting the bits of its code.

XS3 and 8-4-2-1 are examples of self-complementing codes, facilitating error detection and correction.

Error detection and correction capabilities of certain binary codes are discussed, with parity and Hamming codes as examples.

A comprehensive classification of binary codes is presented, covering weighted, non-weighted, sequential, cyclic, and self-complementing codes.

Upcoming videos promise a detailed exploration of the mentioned binary codes, enhancing understanding of their applications.

Engagement is encouraged through the comment section for questions and suggestions, fostering a community of learning.

Transcripts

hey friends

welcome to the youtube channel all about

electronics so in this video

and in the next couple of videos we will

learn about the different

binary codes so first let us understand

what is binary code so this binary code

is a way of representing number letters

or characters

using the group of ones and zeros now

there are different ways

this number or letters can be encoded in

the group of ones and

zeros so over the years different binary

codes have been

evolved but we will see some of the

important binary codes

which are commonly used nowadays so

mainly

the binary codes are classified into the

two categories

that is a numeric binary course and the

alphanumeric binary codes

so the binary codes which are used to

represent the numeric information

or the numbers in the sequence of ones

and zeros are called the numeric codes

while the alphanumeric codes represents

the alphanumeric information

like the letters numbers and the

characters

so this ascii is one of the popular

alphanumeric code

and it is primarily used for

transmitting the data between the

computers and the io devices

such as the printer and the keyboard now

if we talk about the numeric codes

then there are various types of numeric

codes like

obcd8421 code a grey code and the xs3

code

so in the next couple of videos we will

learn about all these binary codes in

detail but first let us briefly talk

about this

bcd code so this bcd stands for binary

coded

decimal and in bcd code each decimal

digit

is encoded into the group of four binary

digits

now there are various types of bcd codes

like

8421 2421 5421

etc but the most common one is the 841

bcd code

so in this 841 bcd code this is how

each decimal digit is encoded well how

each digit is encoded

and what is the meaning of this eight

four two one will get clear to you

very shortly but this eight four two one

is the

weighted code so in general these

numeric codes can be classified as

either a weighted code

or the non-weighted code so this bcd8421

2421 and the 5421 are the few examples

of the

weighted code so the weighted codes are

the one

which obeys the positional weighting

principle meaning that

in this weighted course each position in

the number has some

specific weight for example in this

841 bcd code starting from the msb

the weight of each bit is 8 4 2 and the

1

respectively and the summation of all

these weights

represents the equivalent decimal number

for example

if you take the bcd code 0 1 1 1

then there is a 1 in the position of

this 4 2 and the

1 that means all these ones will get

multiplied by the corresponding

weights and if we add all these weights

then that is the decimal equivalent

number

which is represented by this particular

code

similarly if we take the code 1 0 0 1

then there is a 1 in the position of

this 8 and the 1.

so if we do the summation of all these

weights then it is equal to

9 and there is a decimal equivalent

number which is represented by this

particular code

so basically this 8 4 2 and the 1

represents the weight of each position

and this is how

these 0 to 9 are represented in this 8 4

1 code

so similarly these 5421 is another

weighted code where these 5 4 2 and 1

represents the weight of each position

so for example

if you take the code 1001 then in the

position of 5 and 1 there is a

1 so if we add the weights of each digit

then it is equal to 6 that means this is

how

the decimal number 6 is represented in

this 5 4

1 code and this is how all the digits

starting from 0 to 9

are represented in this 5421 code

now if you see this 8421 or this 5421

code

then here all the weights are positive

that means

these weighted codes are the positive

weighted codes

similarly there are some codes where the

weights of some position is

negative so such codes are known as the

negative weighted codes so this eight

four minus two minus one

is the example of the negative weighted

code

so this is how these decimal digits zero

to nine

are represented in this particular code

so if you see the code

of zero 1 1 1 then in the position of

this 4

minus 2 and the minus 1 there is a 1

so if we add all these weights then the

summation

is equal to 1 that means this code

represents the decimal number 1

similarly

if you see the code 1 0 1 0 then there

is a 1 in the position of this 8 and the

minus 2. so if we do the summation then

the summation is equal to

6 that means this is how this decimal

digit 6

is represented in this particular code

so this 8 4 minus 2 minus 1

is one of the negative weighted codes so

in short

these numeric binary codes could be a

weighted code or the

non-weighted code and further this

weighted code

could be a positive weighted code or the

negative weighted code

and these are the few examples of the

weighted code

now those codes who does not obey the

position weighting principle

are called the non-weighted course and

this xs3

and the gray code are the example of

this non-weighted code

then there are some binary codes which

are the sequential code

so in this sequential code if you see

any binary code

then it is one binary number greater

than the previous code

that means in this sequential code

whenever we add

1 to this particular code then we will

get the next code

and the same is applicable to all other

codes

that means this 8421 is one of the

sequential code

similarly this xs3 code is also example

of the

sequential code so if we just add binary

number 3 to this bcd code

then we will get the equivalent xs3 code

and if you see this access 3 code

then it is also sequential code because

in this code also just by adding a 1 to

the particular code

you will get the next code that means

this 841 bcd code

and the xs3 code are the example of this

sequential codes

then there are some binary codes which

are the cyclic codes

so in a cyclic code a successive code

differs from each other

by only one bit position for example

if you see this grey code then the

successive code

differs by only one bit position for

example

if you take this decimal number 3 and 4

then they are differing by a 1 bit

position over

here likewise if you see the code of

number 9

and 10 then they are also differing by 1

bit over

here so this gray code is the example of

the

cyclic code then the next type of binary

code is the

self-complementing code so first of all

let us understand what is this

self-complementing code

so if we consider the decimal digits

then for any decimal digit

n its ninth complement is equal to nine

minus

n right so for example for the decimal

number one

its ninth complement is equal to eight

likewise for the decimal number 6 its

9th complement

is equal to 3 so in this

self-complementing code

if we have a code for some decimal digit

n then in that code

just by replacing the ones by zeros and

the zeros by one

we will get the equivalent nine's

complement of that particular number

so this xs3 code is the example of the

self-complementing code

so we know that the ninth complement of

the number zero

is equal to nine so if you see over here

then just by replacing the zeros by one

and the ones by zeros

we will get the code of nine likewise

the ninth complement of the decimal

digit three is equal to

6 so in the code of 3 if we just replace

the ones by 0s

and the 0s by 1 then we will get the

equivalent code for the decimal digit

6. so this xs3 is the example of this

self-complementing code then this 8 4

minus 2-1

is another example of this

self-complementing code

and these are the few examples of this

self-complementing code

now if we talk about the classification

of this binary codes

and some binary codes have the

capability of error detection as well as

the correction

so let's take the example of this 841

bcd code

now whenever this code is used in the

digital communication

then during the transmission and the

processing it is susceptible to the

external noise so because of the noise

it is quite possible that

the zero in the code can get replaced by

one and likewise

the one can get replaced by the zero and

if such thing happens

then the error will occur during the

detection for example

while transmitting this code 0 1 0 0 if

due to the noise this last 0 gets

replaced to the 1

and at the receiver it will be received

as 5

and hence the error will occur during

the reception of this

particular code so to detect such error

these error detecting codes are used so

just by adding the parity bit along with

this usual code

it is possible to detect the error

similarly

there are some binary codes which can

even correct the

error so this parity and the hamming

codes

are the example of this error detecting

and the error correcting codes

respectively and here is the complete

classification of the

binary course so in the upcoming video

we will go through some of these binary

codes in detail

but i hope in this video you understood

the different types of

binary codes so if you have any question

or suggestion

then do let me know here in the comment

section below if you like this video hit

the like button

and subscribe the channel for more such

videos