Representation of data and computer arithmetic 2 - JSS2 Computer Studies Past Questions and Answers - page 1

The hexadecimal system holds significance in computing due to its human-readable representation, using 16 digits that include both numerical and alphabetical characters. This characteristic makes it more convenient for programmers and system designers to work with binary data, enhancing readability and reducing complexity. The practical applications of binary-coded systems, such as Gray Code and Excess-3, are notable in digital circuits and communication technologies. Gray Code minimizes errors during binary counting, crucial in applications like rotary encoders. Excess-3, on the other hand, is commonly employed in digital circuits and calculators for its representation of decimal digits by adding 3 to their binary equivalents. These binary-coded systems play key roles in optimizing data processing, storage, and communication within the realm of computing.

The hexadecimal system, with sixteen digits (0-9 and A-F), complements the binary system by offering a more human-readable and concise representation of binary data. Each digit in hexadecimal represents a power of 16, allowing for a compact expression of large binary numbers. For example, the rightmost digit has a weight of 16^0, the next to the left has a weight of 16^1, and so on.

Binary Coded Decimal (BCD) is a binary representation of decimal numbers, where each decimal digit is represented by its binary equivalent. BCD simplifies the conversion between binary and decimal, allowing for straightforward representation of numerical data in digital circuits and systems.

Gray Code is a binary numeral system crucial in applications where minimizing errors during binary counting is essential, such as in rotary encoders. Unlike traditional binary counting, in Gray Code, two successive values differ in only one bit, reducing the chance of errors during counting. For instance, the transition from 0110 to 1110 in Gray Code involves changing only one bit.

Excess-3 Code, also known as XS-3, represents decimal digits by adding 3 to their binary equivalents. This coding scheme is commonly used in digital circuits and calculators. By adding 3 to the binary representation of each decimal digit, Excess-3 Code simplifies arithmetic operations and reduces the likelihood of errors in calculations.