Explain the Binary, Octel, Decimal, and Hexadecimal number systems with examples in detail.

Number Systems:

Binary Number System:

The binary number system is a base 2 system that uses only two digits (0 and 1). Each digit is referred to as a bit. A single bit can represent two values, 0 and 1, and all numbers in the binary number system are represented by combinations of 1s and 0s. For example, the binary number 101 is represented as 1 four, 0 twos, and 1 one, or 4 + 0 + 1 = 5.

Octal Number System:

The octal number system is a base 8 system that uses eight digits (0-7). The octal number system is commonly used in programming languages and is sometimes referred to as the base-8 number system. Each digit in an octal number can represent three values (0-7), and all numbers in the octal number system are represented by combinations of these digits. For example, the octal number 12 is represented as 1 eight and 2 ones, or 8 + 2 = 10.

Decimal Number System:

The decimal number system is a base 10 system that uses ten digits (0-9). The decimal number system is the most commonly used number system and is sometimes referred to as the base-10 number system. Each digit in a decimal number can represent ten values (0-9), and all numbers in the decimal number system are represented by combinations of these digits. For example, the decimal number 23 is represented as 2 tens and 3 ones, or 20 + 3 = 23.

Hexadecimal Number System:

The hexadecimal number system is a base 16 system that uses sixteen digits (0-9 and A-F). The hexadecimal number system is commonly used in computing and is sometimes referred to as the base-16 number system. Each digit in a hexadecimal number can represent sixteen values (0-9 and A-F), and all numbers in the hexadecimal number system are represented by combinations of these digits. For example, the hexadecimal number 1A is represented as 1 sixteen and 10 ones, or 16 + 10 = 26.