1.1 Mathematical Data Types

In this section, you learned that all data in computing is represented using mathematical data types that determine how values are stored, interpreted, and processed. You examined integers, which are used for counting, indexing, and control flow, and real numbers, which include both rational and irrational values and are stored approximately using floating-point representation based on the IEEE 754 standard. You also learned how floating-point numbers use a sign bit, exponent, and mantissa to balance range and precision. In addition, you explored characters and strings, which represent textual data using numeric encoding standards such as ASCII and Unicode, as well as Boolean values, which represent true or false states and form the basis of logic and decision-making in programs. Finally, you were introduced to composite types such as tuples and arrays, which group related data values for use in real-world computing applications.

1.2 Representations of Numbers in Computers: Binary, Hexadecimal

In this section, you learned that computers use the binary number system, which represents data using only the digits 0 and 1 and is based on powers of 2. You saw how binary numbers are used to convey values, characters, instructions, and on/off states in digital systems, and why binary is efficient for machines but difficult for humans to interpret. To address this, you studied the hexadecimal number system, which is a base-16 representation that uses digits 0 to 9 and the letters A to F, with each hexadecimal digit corresponding to four binary bits. You explored how hexadecimal provides a compact, human-readable way to represent binary data and is commonly used in memory addresses, debugging, machine-level programming, and web colour codes.

1.3 Hexadecimal, Binary Conversions and Arithmetic Operations

In this section, you learned how to convert between binary and hexadecimal by grouping binary digits into sets of four and replacing hexadecimal digits with their 4-bit binary equivalents. You practiced binary arithmetic, including addition and subtraction, using base-2 rules for carrying and borrowing, and you learned how to verify results by converting them to decimal. You also explored hexadecimal arithmetic, which is frequently used in low-level programming, networking, and hardware applications, and is often performed by converting values to binary or decimal before completing calculations. These conversion and arithmetic skills are essential for tasks such as memory analysis, checksum verification, and debugging, and they support a deeper understanding of how data is stored and processed in digital systems.