 The hexadecimal system is a numbering system that uses base 16. It uses the digits from 0 to 9, as well as the letters A to F to represent values from 10 to 15. This allows for a more compact and human-readable representation of binary numbers.

In computing, the hexadecimal system is often used to represent memory addresses and binary values, as it provides a more concise representation than binary.

For example, the binary number 10101011 can be represented in hexadecimal as AB.

The hexadecimal system is particularly useful in the field of programming and computer science, as it facilitates the manipulation and understanding of binary values.

Transcoding refers to the process of converting or transforming data from one format or encoding scheme to another. This can apply to various types of data, including text, images, audio, or video.

In the context of digital media:

1. Text Transcoding: Converting text from one character encoding (like ASCII, UTF-8, etc.) to another.
2. Image Transcoding: Changing the format or compression method of an image (e.g., converting from JPEG to PNG).
3. Audio Transcoding: Converting audio data from one codec to another (e.g., from MP3 to AAC).
4. Video Transcoding: Changing the format or compression of a video file (e.g., from AVI to MP4).

Transcoding is important in various scenarios, such as adapting media for different devices, reducing file sizes, or ensuring compatibility between different systems and software.

Converting from decimal to another base involves representing the number using the digits of the chosen base . Here are the steps to perform this conversion:

1. Divide the decimal number by the base : Divide the decimal number by the base and record the quotient and the remainder.
2. Continue the division: Use the quotient obtained in the previous step as the new number to be divided by the base . Record the new quotient and the new remainder.
3. Repeat the process: Continue dividing the quotient obtained at each step until the quotient becomes zero.
4. Read the remainders in reverse: The remainders obtained at each step constitute the digits of the representation of the number in base , read in reverse order.
5. Write the number in base : Write down the obtained remainders in reverse order to get the representation of the number in base .

Example:

Let’s convert the decimal number 73 to base 2 (binary).

1. 73 divided by 2 gives a quotient of 36 and a remainder of 1.
2. 36 divided by 2 gives a quotient of 18 and a remainder of 0.
3. 18 divided by 2 gives a quotient of 9 and a remainder of 0.
4. 9 divided by 2 gives a quotient of 4 and a remainder of 1.
5. 4 divided by 2 gives a quotient of 2 and a remainder of 0.
6. 2 divided by 2 gives a quotient of 1 and a remainder of 0.
7. 1 divided by 2 gives a quotient of 0 and a remainder of 1.

Reading the remainders in reverse, we get 1001001. Thus, 73 in base 10 is equivalent to 1001001 in base 2 (binary).