Explain data representation, the binary and decimal number systems, and decision support systems.

a) Data representation refers to the methods used to encode and store data in a computer system. All data, such as numbers, text, images, and audio, must be converted into a binary format (0s and 1s) that the computer's hardware can process and understand. This conversion allows for efficient storage, processing, and transmission of information within digital systems.

b)

i) The binary number system uses a base of 2, meaning it only uses two digits: 0 and 1. In contrast, the decimal number system uses a base of 10, employing ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

ii) In the binary system, each digit's place value is a power of 2 (e.g., $2^0, 2^1, 2^2$), while in the decimal system, each digit's place value is a power of 10 (e.g., $10^0, 10^1, 10^2$). This means that a larger number of digits is often required to represent the same value in binary compared to decimal.

c) A Decision Support System (DSS) is an information system that aids management in making decisions by analyzing data and presenting it in an easily understandable format. It typically combines data, analytical models, and user-friendly software to help users evaluate various alternatives and choose the best course of action for complex, non-routine problems.