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# Definition | Types of Number Systems in Maths

## What are Number Systems?

Number systems provide a way to represent quantities and values using a unique set of symbols. The most commonly used number system is the decimal system, which uses ten digits (0-9). However, computers and digital systems use other number systems such as binary, octal, and hexadecimal. ## Types of Number Systems

There are several types of number systems, including

• Binary number system (Base – 2)
• Octal number system (Base – 8)
• Decimal number system (Base – 10)
• Hexadecimal number system (Base – 16)

## Decimal Number System

The decimal system is the most familiar and widely used number system, which uses ten digits (0-9). Each digit represents a value that is a power of 10.

For example, in the number 123, the digit 1 represents 100, the digit 2 represents 20, and the digit 3 represents 3. Therefore, the value of 123 is 1 x 100 + 2 x 10 + 3 x 1 = 123.

## Binary Number System

The binary system uses only two digits, 0 and 1. It is the foundation of all digital computing systems. Each digit in a binary number represents a power of 2.

For example, in the binary number 1011, the digit 1 represents 2^3, the digit 0 represents 2^2, the digit 1 represents 2^1, and the digit 1 represents 2^0. Therefore, the value of 1011 in binary is 1 x 2^3 + 0 x 2^2 + 1 x 2^1 + 1 x 2^0 = 11 in decimal.

## Octal Number System

The octal system uses eight digits (0-7). Each digit in an octal number represents a power of 8.

For example, in the octal number 73, the digit 7 represents 8^1, and the digit 3 represents 8^0. Therefore, the value of 73 in octal is 7 x 8^1 + 3 x 8^0 = 59 in decimal.

The hexadecimal system uses 16 digits (0-9 and A-F). Each digit in a hexadecimal number represents a power of 16. The letters A through F represent values 10 through 15.

For example, in the hexadecimal number AB2, the digit A represents 10 x 16^2, the digit B represents 11 x 16^1, and the digit 2 represents 2 x 16^0.

Therefore, the value of AB2 in hexadecimal is 10 x 16^2 + 11 x 16^1 + 2 x 16^0 = 2738 in decimal.

## Conversion of Number Systems

### Converting Binary to Decimal Number System: A Step-by-Step Guide

Binary is a base-2 number system, while decimal is a base-10 number system. Converting a binary number to a decimal number may seem challenging, but with the following steps, it’s easy to do.

##### Step 1: Write down the binary number

The first step is to write down the binary number that you want to convert. For example, let’s convert the binary number 1011 to decimal.

##### Step 2: Assign powers of 2 to each digit

Starting from the right side of the binary number, assign powers of 2 to each digit. The rightmost digit has a power of 2^0, the next digit has a power of 2^1, the next has a power of 2^2, and so on.

For example, for the binary number 1011, the rightmost digit (1) has a power of 2^0, the next digit (1) has a power of 2^1, the next digit (0) has a power of 2^2, and the leftmost digit (1) has a power of 2^3.

##### Step 3: Multiply each digit by its corresponding power of 2

Next, multiply each digit by its corresponding power of 2.

For example, for the binary number 1011, we have:

1×2^3 + 0x2^2 + 1×2^1 + 1×2^0

##### Step 4: Add the products together

Finally, add the products together to get the decimal equivalent of the binary number. Continuing from the previous step, we have:

1×2^3 + 0x2^2 + 1×2^1 + 1×2^0 = 8 + 0 + 2 + 1 = 11

Therefore, the binary number 1011 is equivalent to the decimal number 11.

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