Final answer:
Binary, octal, and hexadecimal number systems are used in computing and digital electronics, where binary is base-2, octal is base-8, and hexadecimal is base-16. These allow for efficient data representation across various platforms.
Step-by-step explanation:
Understanding Binary, Octal, and Hexadecimal Number Systems
The number systems binary, octal, and hexadecimal are significant in the field of computing and digital electronics. The binary system is the fundamental language of computers, utilizing only two digits, 0 and 1. Each digit in this system represents a power of 2. The octal system uses eight digits, ranging from 0 to 7, and each place value is based on a power of 8. The hexadecimal system comprises sixteen symbols, 0-9 and the letters A to F, with each position representing a power of 16. These number systems are essential for representing data in various formats within computers and electronic devices.
To convert numbers between these systems, one must understand their respective base systems: binary is base-2, octal is base-8, and hexadecimal is base-16. For example, the binary number 1101 corresponds to the decimal number 13, the octal number 15, and the hexadecimal number D. Understanding these systems allows for the efficient representation and processing of data in computing and digital systems.