Revise Data Representation for Cambridge 9618 (1.1)

We are accustomed to the denary (base-10) number system, which uses ten digits (0-9). Computers, however, operate on the binary (base-2) system, using only two digits: 0 and 1. Each digit in a binary number is a 'bit'. To make long binary strings more manageable for humans, we often use the hexadecimal (base-16) system. Hexadecimal uses 16 symbols: the digits 0-9 and the letters A-F (representing 10-15).

Representing negative numbers in binary requires a special system. A simple approach might be to use one bit for the sign (e.g., 0 for positive, 1 for negative), known as sign-and-magnitude. However, this method has issues, including two different representations for zero (+0 and -0) and complex arithmetic logic. The standard method used by modern computers is Two's Complement. In this system, the most significant bit (MSB) of a number indicates its sign (0 for positive, 1 for negative), but it also carries a negative place value. This results in a single representation for zero and makes binary addition and subtraction straightforward for both positive and negative numbers.

Computers must also represent text. This is achieved by assigning a unique binary code to each character. A 'character set' is the collection of characters and their corresponding codes. The earliest widespread standard was ASCII (American Standard Code for Information Interchange), which uses 7 bits to represent 128 characters, including uppercase and lowercase English letters, numbers, and punctuation. Extended ASCII uses 8 bits for 256 characters. However, ASCII is insufficient for global languages. Unicode is the modern standard, designed to represent characters from virtually all writing systems. It can use up to 32 bits per character, allowing for over a million unique codes. UTF-8 is a popular and efficient way of encoding Unicode characters, using a variable number of bytes.