Numbers in base 16 are called as:
A) Octal System
B) Hexadecimal System
C) Decimal System
D) Binary System
Answer: B) Hexadecimal System
Hexadecimal System: The hexadecimal system, also known as base-16 or simply hex, is a positional numeral system that uses a radix (base) of 16. Unlike the decimal system representing numbers using ten symbols, hexadecimal uses sixteen distinct symbols, most often the symbols "0"–"9" to represent values 0 to 9, and "A"–"F" (or alternatively "a"–"f") to represent values from ten to fifteen.
Octal System: The octal, or oct for short, is the base-8 positional numeral system. This means it uses a base of 8 and includes only digits from 0 to 7 to represent numbers. It differs from the more familiar decimal system (base 10) which uses digits from 0 to 9, and the hexadecimal system (base 16) which uses digits and letters from 0 to 9 and A to F.
Some key points about the octal system:
- Positional system: The value of each digit in an octal number depends on its position. Just like in the decimal system, the rightmost digit represents the ones place, the next digit to the left represents the eights place (8^1), the next digit represents the sixty-fours place (8^2), and so on.
- Counting in octal: After 7, the next number in octal isn't 8, but instead rolls back to 0 and the next position increases by 1. So, the sequence goes 0, 1, 2, 3, 4, 5, 6, 7, 10 (eight), 11, 12, 13, 14, 15, 16 (sixty-four), 17, etc.
- Applications: In the past, the octal system was more commonly used in computing because each octal digit corresponds to three binary digits. This made it convenient for representing binary data in a more compact form than using straight binary notation. However, nowadays, hexadecimal (base-16) has largely replaced octal for this purpose.
Decimal System:
- Base-10 system: This means it uses a base of 10. Unlike binary (base-2) or hexadecimal (base-16), it only needs 10 different symbols to represent all numbers.
- Symbols: 10 digits - 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 - are used to represent all integers (whole numbers).
- Positional notation: The value of each digit depends on its position within the number. The rightmost digit is the ones place, the next digit to the left is the tens place (10^1), the next is the hundreds place (10^2), and so on.
Binary System:
- Base-2 system: Uses a base of 2, meaning it only needs two digits to represent all numbers. Unlike decimal (base-10) with 10 digits, binary uses 0 and 1.
- Positional notation: Similar to decimal, the value of each digit depends on its position. The rightmost digit is the ones place (2^0), the next digit to the left is the twos place (2^1), and so on.
- Bits and bytes: Individual digits are called bits. A group of 8 bits forms a byte, the basic unit of storage in computers.