Question

How many binary digits would it take to represent the following phrase in ASCll code? In 16-bit Unicode? (Do not include the " " marks.) "Invitation to Computer Science"

Short answer

240 bits for ASCII, 480 bits for Unicode.

Step-by-step solution

Count the Characters

To determine the number of binary digits, first count the characters in the given phrase: "Invitation to Computer Science". This includes letters, spaces, and punctuation. This phrase has 30 characters.

Calculate ASCII Binary Digits

In ASCII, each character is represented by 7 or 8 bits (commonly 8 bits for convenience). With 8 bits per character and 30 characters, the total number of bits required is calculated as follows: \[ 30 \text{ characters} \times 8 \text{ bits/character} = 240 \text{ bits} \]

Calculate Unicode Binary Digits

In 16-bit Unicode, each character is represented by 16 bits. Therefore, for 30 characters, the total number of bits required is: \[ 30 \text{ characters} \times 16 \text{ bits/character} = 480 \text{ bits} \]

Key concepts

ASCII code

ASCII stands for American Standard Code for Information Interchange. It's one of the earliest character encoding schemes, developed to standardize the representation of characters using binary digits.

Here's what you need to know about ASCII:

• ASCII code uses 7 bits to represent 128 possible characters, including English letters (uppercase and lowercase), digits, and some special symbols.
• In practice, ASCII is often expanded to use 8 bits (1 byte) which allows for 256 characters, making it convenient for computer operations.
• Its simplicity makes it very important for early computing and remains in use as a fundamental element of various encoding systems today.

In our exercise, each character of the phrase "Invitation to Computer Science" is represented by 8 bits in ASCII. This cumulative representation leads to a total of 240 binary digits for the 30 characters.

Unicode representation

Unicode is a universal character encoding standard designed to represent all the world’s writing systems. While ASCII code is limited, Unicode expands how characters are represented in computing environments.

Important aspects of Unicode include:

• Unicode can support over 143,000 characters from different languages and scripts, as well as symbols and emojis, because it uses a multi-byte structure.
• In basic terms, Unicode assigns a unique code point to every character and can range from 8-bit to 32-bit representations depending on the version (such as UTF-8, UTF-16, etc.).
• In our exercise, we're considering 16-bit Unicode, which uses 16 bits (or 2 bytes) per character – double the space compared to ASCII.

This means that for the same phrase, "Invitation to Computer Science," using Unicode requires 480 binary digits.

bit calculation

Bit calculation is the process of determining the number of binary digits needed to encode information. In character encoding, understanding how many bits are used per character helps in computing the total storage or transmission size of text data.

To perform bit calculations:

• Determine the number of characters in your text. Include every letter, space, and punctuation mark.
• Identify the encoding scheme to use (e.g., ASCII or Unicode) and note the bits required per character.
• Multiply the number of characters by the bits per character to get the total bits required.

For instance, the phrase "Invitation to Computer Science" with ASCII encoding needs 30 characters × 8 bits/character = 240 bits. In 16-bit Unicode, it requires 30 × 16 = 480 bits.

character encoding

Character encoding is the method of converting characters into a format that can be easily stored and processed by computers. Different encoding schemes have evolved to meet the needs of various languages and symbols found in the digital age.

When choosing a character encoding scheme, keep in mind:

• Encoding schemes like ASCII are efficient for English texts and minimal additional symbols but are limited in their capacity for other language scripts.
• Unicode is preferred for global compatibility because it supports a vast array of characters and symbols from multiple languages around the world.
• The choice of encoding affects storage requirements and compatibility with different software and platforms.

In essence, understanding encoding helps in effectively handling data across diverse systems, ensuring the correct portrayal and integrity of text information.