Question

A binary file is 4560 bytes long. How long will it be if encoded using base64 encoding, with a CR+LF pair inserted after every 110 bytes sent and at the end?

Short answer

The encoded binary file will be 6192 bytes long.

Step-by-step solution

Calculate Base64 Encoded Size

Base64 encoding converts 3 bytes of binary data into 4 characters. Thus, if a file is 4560 bytes, the formula for conversion is \( \lceil \frac{4560 \times 4}{3} \rceil \). Performing the calculation, \( \frac{4560 \times 4}{3} = 6080 \) characters.

Calculate Number of CR+LF Pairs

A CR+LF pair (carriage return and line feed) is 2 bytes. For every 110 characters of encoded data, a CR+LF pair is added. Since the encoded data is 6080 characters, calculate how many CR+LF pairs will be needed: \( \frac{6080}{110} = 55.27 \). Thus, we will need 55 CR+LF pairs in the body and 1 at the end, totaling 56 pairs.

Calculate Total Size of Encoded Data

Multiply the number of CR+LF pairs by their size (2 bytes per pair), and add it to the size of the base64 data: \( 6080 + (56 \times 2) = 6192 \) bytes, which is the total size of the file including the CR+LF pairs.

Key concepts

Binary File

A binary file is a file that contains data in a format that is not human-readable but is readable by a computer. Unlike text files that store data as plain text, binary files store data in consecutive bytes. This means that binary files can include any form of data such as images, videos, executables, or any other type of structured or unstructured data.
Binary files are crucial because they allow computers to understand and process a wide range of data types. Here are some key aspects of binary files:

• They tend to be more space-efficient than text files for storing the same data.
• They must be opened and read by specific software or programs that understand their structure.
• Common extensions for binary files include .bin, .exe, or .dat, among others.

To further manipulate binary files, understanding character encoding is essential.

Character Encoding

Character encoding is a system that pairs a set of characters, like letters and numbers, with something else, such as numeric codes, which allows computers to store and process text efficiently. Common character encoding systems include ASCII, UTF-8, and UTF-16.
Base64 encoding is a specific type of character encoding used to encode binary data into a text format. Each set of 3 bytes from the binary file is transformed into 4 encoded characters. Here’s why character encoding is important:

• It ensures that text is correctly displayed and interpreted across different devices and platforms.
• In Base64 encoding, the outcome is always text that only includes ASCII characters, which are more universally supported.
• Prevents data corruption in environments that only support text, which is common in email and data transmission protocols.

By understanding character encoding, students will better grasp the implications of encoding a binary file into another format for various applications, including data transmission.

Data Transmission

Data transmission entails the transfer of data between devices, which can include computers, phones, and other digital devices over a network. This process can happen via wires or wirelessly and plays a huge role in communication and data sharing.
During the data transmission process, Base64 encoding is commonly used for sending binary files in a text-based form. Here are some of its roles:

• It ensures that binary data is safely sent through systems that may not handle binary data well, avoiding issues caused by non-text data misinterpretation.
• Base64 increases the size of the data being sent, as each 3 bytes of binary are turned into 4 bytes of Base64 data. This is an important consideration during transmission.
• It's especially pivotal during email transmission where text-based formats are prioritized.

Understanding data transmission is essential for evaluating the impact of different encoding methods on bandwidth and transmission speeds.

File Size Calculation

File size calculation is the process of determining how much storage space a file occupies. This is important for understanding file requirements and limitations, and it affects how files are transmitted or stored.
When calculating the file size after encoding using Base64, several factors need to be considered:

• The Base64 encoding itself increases the size of the original file by about 33% due to its conversion rate. For example, encoding 4560 bytes will result in 6080 bytes due to the conversion of 3 bytes to 4 characters.
• Additional bytes may need to be considered when including carriage return and line feed pairs (CR+LF). These are often used to structure data into more manageable sections for transmission.
• Finally, the cumulative file size includes both the encoded data and any additional bytes from structures like CR+LF.

Accurate file size calculations ensure efficient and effective data storage and transmission strategies.