Number System in Maths

What are Number Systems with Examples?

Number systems are methods of representing numbers using symbols or digits. Here are the number systems with examples:

1. Decimal (Base-10): Uses digits 0-9. Example: 456.
2. Binary (Base-2): Uses digits 0 and 1. Example: 1010.
3. Octal (Base-8): Uses digits 0-7. Example: 64.
4. Hexadecimal (Base-16): Uses digits 0-9 and letters A-F. Example: 1A3.
5. Roman Numerals: Uses letters to represent values. Example: IX, XIV, CXXV.

What are Different Types of Number Systems?

There are several types of number systems, each with its own base and representation. Here are the main ones:

1. Decimal Number System (Base-10): Uses digits 0 through 9, with each place value representing a power of 10.
2. Binary Number System (Base-2): Uses digits 0 and 1, with each place value representing a power of 2.
3. Octal Number System (Base-8): Uses digits 0 through 7, with each place value representing a power of 8.
4. Hexadecimal Number System (Base-16): Uses digits 0 through 9 and letters A through F (representing values 10 through 15), with each place value representing a power of 16.
5. Roman Numeral System: Uses specific letters to represent values, with various rules for addition and subtraction.

What are Conversion Rules of Number Systems?

Here are the conversion rules for common number systems:

1. Decimal to Binary:
   • Divide the decimal number by 2.
   • Write down the remainder.
   • Repeat the process with the quotient until it becomes 0.
   • The binary equivalent is obtained by reading the remainders in reverse order.
2. Binary to Decimal:
   • Write down the binary number.
   • Assign each digit a place value, starting from the rightmost digit (1, 2, 4, 8, …).
   • Multiply each digit by its corresponding place value.
   • Add up all the products to get the decimal equivalent.
3. Decimal to Octal:
   • Divide the decimal number by 8.
   • Write down the remainder.
   • Repeat the process with the quotient until it becomes 0.
   • The octal equivalent is obtained by reading the remainders in reverse order.
4. Octal to Decimal:
   • Write down the octal number.
   • Assign each digit a place value, starting from the rightmost digit (1, 8, 64, …).
   • Multiply each digit by its corresponding place value.
   • Add up all the products to get the decimal equivalent.
5. Decimal to Hexadecimal:
   • Divide the decimal number by 16.
   • Write down the remainder.
   • Repeat the process with the quotient until it becomes 0.
   • For remainders greater than 9, represent them with corresponding hexadecimal letters (A for 10, B for 11, etc.).
   • The hexadecimal equivalent is obtained by reading the remainders in reverse order.
6. Hexadecimal to Decimal:
   • Write down the hexadecimal number.
   • Assign each digit a place value, starting from the rightmost digit (1, 16, 256, …).
   • Multiply each digit by its corresponding place value.
   • Add up all the products to get the decimal equivalent.

Number System is a method of representing numbers on the number line with the help of a set of Symbols and rules. These symbols range from 0-9 and are termed as digits. Let’s learn about the number system in detail, including its types, and conversion.