What is the binary representation of the hexadecimal number 2F?

The binary representation of the hexadecimal number 2F is 0010 1111.

To convert a hexadecimal number to binary, each hexadecimal digit is replaced by its binary equivalent. Hexadecimal is a base-16 number system, while binary is a base-2 system. The hexadecimal system uses the digits 0-9 and the letters A-F to represent the numbers 0-15. In binary, these numbers are represented by four digits.

The hexadecimal number 2F has two digits: 2 and F. The binary equivalent of 2 in hexadecimal is 0010. The letter F represents the number 15 in hexadecimal, and its binary equivalent is 1111. Therefore, when you replace each hexadecimal digit in 2F with its binary equivalent, you get 0010 1111.

This conversion is straightforward because hexadecimal and binary are both positional numeral systems, and 16 is a power of 2. This means that each hexadecimal digit can be directly mapped to a unique four-digit binary number. This relationship makes it easy to convert between these two systems, which is often necessary in computer science because computers use binary to process data, but hexadecimal is more compact and easier for humans to read and write.

Understanding these conversions is crucial for grasping the fundamentals of computer operations and how data is processed at the CPU level. For further study on numerical systems used in computing, explore the comprehensive overview of binary and number systems.

A-Level Computer Science Tutor Summary: The hexadecimal number '2F' converts to the binary '0010 1111'. Each hexadecimal digit is directly translated to a four-digit binary number because the base-16 system aligns perfectly with the base-2 system. This makes the conversion simple and efficient, useful in computing where binary is prevalent but hexadecimal provides a more compact format for human use.