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Chapter 1: Problem 12

What amount of memory is enough to store a letter of the alphabet or a small number?

Short Answer

Expert verified
Answer: 1 byte (8 bits) of memory is required to store a letter of the alphabet or a small number (0-9) using ASCII or UTF-8 encoding.

Step by step solution

01

Understand the character encoding

Characters and numbers are represented in computer systems using encoding schemes to convert them into binary codes. A widely used encoding is called the American Standard Code for Information Interchange (ASCII). ASCII uses 7 bits for representing characters, allowing for 128 different characters, which includes the 26 lowercase letters, 26 uppercase letters, 10 digits (0-9), and other special characters and control codes.
02

Calculate the memory required with ASCII encoding

As mentioned earlier, ASCII uses 7 bits to represent a character. However, in practice, one byte (8 bits) is typically used in most computer systems to store an ASCII character. This is because modern computers have a byte-addressable memory architecture, and one byte is the smallest addressable unit of memory. Therefore, one byte (8 bits) of memory is enough to store a letter of the alphabet or a small number.
03

Consider other character encodings

While ASCII is a widely used encoding, there are other popular character encodings, such as Unicode, which is designed to support a larger character set for languages around the world. The most common representation of Unicode characters is UTF-8, which uses a variable number of bytes (1 to 4 bytes) to store a character. However, for English alphabet letters and small numbers (0-9), UTF-8 also uses 1 byte to represent them, similar to ASCII.
04

Conclusion

Both commonly used character encodings, ASCII and UTF-8, require 1 byte (8 bits) of memory to store a letter of the alphabet or a small number (0-9).

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