Question

A 100 -byte ASCII string is encoded using base64. How long is the resulting string?

Short answer

The base64 encoded string is 136 characters long.

Step-by-step solution

Understand Base64 Encoding Process

In base64 encoding, each group of 3 bytes of the input data (24 bits) is divided into 4 groups of 6 bits, each of which is represented by a character from the base64 alphabet. Thus, each 3 bytes of input becomes 4 base64 characters.

Calculate Number of Base64 Characters

Since each 3-byte chunk of original data turns into 4 characters in base64, for 100 bytes, we first determine how many full groups of 3 can be formed. We divide 100 bytes by 3 to get 33 full groups with 1 leftover byte (since \(100 \div 3 = 33 \) remainder 1).

Account for Padding

Each complete group of 3 bytes contributes 4 base64 characters, which results in \(33 \times 4 = 132\) characters. For the remaining 1 byte, base64 encoding requires padding to make a full 3-byte group, typically with `=` characters. One byte will require 2 padding characters, resulting in 4 characters from that section as well (2 character from encoding and 2 padding characters).

Summing Up Total Length

The total length of the base64 encoded output is the sum of the characters from the full 3-byte groups and the padded section. Therefore, it is \(132 + 4 = 136\) characters.

Key concepts

ASCII string

ASCII, which stands for American Standard Code for Information Interchange, is a character encoding standard used to represent text in computers and other devices that use text. Each character in an ASCII string is represented by a single byte, and there are 128 characters in the standard ASCII table.

• Each character corresponds to a number between 0 and 127.
• These numbers represent various characters, such as letters, numbers, punctuation marks, and control characters.

When encoding a 100-byte ASCII string, you essentially have 100 characters, since each ASCII character takes up one byte. This foundational understanding is crucial when considering how data is handled during the encoding processes like base64.

encoding process

The base64 encoding process is a method designed to represent binary data in an ASCII string format by translating it into a radix-64 representation. It is especially useful for data transmission in environments that only support text.

• Base64 transforms every 3 bytes (24 bits) from the input into 4 base64 characters (each character representing 6 bits).
• This is done by splitting the 24 bits into four 6-bit chunks, where each chunk maps to a character in the base64 alphabet.

The alphabet used for this encoding includes uppercase letters (A-Z), lowercase letters (a-z), digits (0-9), and two additional symbols (+ and /). This ensures that the output consists only of characters found in the ETI (Extended Latin Alphabet), avoiding potential misinterpretations when viewed as plain text.

byte calculation

The byte calculation in base64 encoding helps determine how many base64 characters are produced from the original data. For example, if you have a 100-byte ASCII string:

• Each group of 3 bytes (or 24 bits) from the input converts to 4 base64 characters.
• Since 100 divided by 3 results in 33 full groups with a remainder, there are 33 groups of 3 bytes and 1 leftover byte.

Therefore, these full groups become 132 characters (33 groups × 4 characters per group) as they translate into base64 format. Consideration of the leftover bytes is crucial to accounting for padding, which the next section will discuss.

padding in encoding

Padding is a vital part of the base64 encoding process, ensuring that the output string is a multiple of 4 characters. This is especially relevant when your input data doesn't cleanly divide into 3-byte chunks.

• When the input byte count isn't a multiple of three, base64 adds padding using the `=` character to bring the character count up to a multiple of 4.
• For instance, if you have 1 leftover byte after dividing your data into triplets, it will be padded to mimic 3 bytes by adding 2 `=` characters, ensuring all segments are treated equally.

So, for our 100-byte ASCII string example, the 1 byte leftover results in an additional 4 characters: 2 from encoding that byte, plus 2 padding characters, for a total of 136 characters in the base64 encoded string.