A Binary number is represented by 0's and 1's. The binary number is be converted into possible other three number system that are

- Binary to Decimal
- Binary to Octal
- Binary to Hexadecimal

## Binary to Decimal

For converting a binary number into a decimal number, we are using the following steps that are:

**Step 1**

Start from the least significant bit. Multiply each bit of binary number with the corresponding positional base value. The base value of binary numbers is 2.

**Step 2**

Next, sum up all products.

**Step 3**

Finally, get the total value that is the resulting decimal value.

For example:To covert the binary number(1011)_{2}into decimal number.Step 1:Start at the least significant bit. Write the positional value for each digit. (1011)_{2}. Positional base value for 1st position from the right is 2^{0}. Positional base value for 2nd position from the right is 2^{1}. Positional base value for 3rd position from the right is 2^{2}. Positional base value for 4th position from the right is 2^{3}. Let us multiply positional base value with the corresponding binary digit (1011)_{2}====> 1 * 2^{3}+ 0 * 2^{2}+ 1 * 2^{1}+ 1 * 2^{0}Step 2:When you Multiply each binary bit with its positional value, you get the result as follows: (1011)_{2}====> 1 * 8 + 0 * 4 + 1 * 2 + 1 * 1Step 3:Add all the products. (1011)_{2}====> 8 + 0 + 2 + 1 = 11 The decimal value of the binary number (1011)_{2}is (11)_{10}.

## Binary to fractional decimal number

If the number is a fractional part of the binary number, that is converted into a fractional part of the decimal number.

**Step 1:**

Start after the fractional point. Multiply each binary digits with the corresponding positional value.

**Step 2:**

Add all the product for getting fractional decimal value.

For exampleTo convert binary(0.1010)_{2}into decimalStep 1:Multiply each binary digits with the corresponding positional value. Positional base value of the 1st digit after decimal point is 2^{-1}Positional base value of the 2nd digit after decimal point is 2^{-2}Positional base value of the 3rd digit after decimal point is 2^{-3}Positional base value of the 4th digit after decimal point is 2^{-4}3(0.1010)_{2}====> 1 * 2^{-1}+ 0 * 2^{-2}+ 1 * 2^{-3}+ 0 * 2^{-4}(0.1010)_{2}====> 1 * 1/2^{1}+ 0 * 1/2^{2}+ 1 * 1/2^{3}+ 0 * 1/2^{4}Step 2:Add all the product for getting fractional decimal value. (0.1010)_{2}====> 0.5 + 0 + 0.125 + 0 = (0.625)_{10}The decimal value for the binary number(0.1010)_{2}is (0.625)_{10}

## Binary to Octal number

A group of 3 bits of binary digits is equal to one digit octal digit. The following steps are used for binary to octal conversion.

**Step 1:**

Divide the binary number into a group of 3 bits on both sides of the binary point. If any group does not have 1 or 2 bits, we need to add the required number of zeros on the end of both sides of the binary point.

**Step 2:**

Next, write the corresponding octal value for each group of the binary number

For example:To convert Binary number(10111)_{2}into Octal.Step 1:Break the whole binary into group of three bits (10111)_{2}======> 10 111 Add one zero on the left (010) (111)Step 2:Write the corresponding octal value 111 =7, 010 =2 (010) (111) ====> 2 7 (10111)_{2}=(27)_{8}The equivalent octal value for the binary(10111)2 is (27) _{8}

## Binary to Hexadecimal number

Binary to Hexadecimal number conversion is simple and similar to octal conversion. A group of 4 binary bits is equal to 1 hexadecimal digit.

**Step 1:**

Divide the binary number into a group of 4 bits on both sides of the binary point. If any group does not have 1 or 2 or 3 bits, we need to add the required number of 0s on the end of both sides of the binary point.

**Step 2:**

Next, write the corresponding hexadecimal value for each group.

For example:1. To convert Binary number(1010111)_{2}into hexadecimal.Step 1:Divide it into a group that has four bits (1010111)_{2}======> 101 0111 Add one zero on the left to make a group (0101) (0111)Step 2:Write the corresponding hexadecimal value for each group for 0101 =5, and 0111 =7 (0101) (0111)====> 5 7 (1010111)_{2}=(57)_{16}The equivalent hexadecimal value for the binary(1010111)2 is (57) _{16}2. To convert Binary number(1110101.001)_{2}into hexadecimal.Step 1:Divide it into a group that has 4 bits (1110101.001)_{2}======> 111 0101 . 001 Add one zero on both sides of the binary point to make a group (0111) (0101).(0010)Step 2:Write the corresponding hexadecimal value for each group for 0111 = 7, 0101 = 5, and 0010 = 2 (0111) (0101).(0010)===> 7 5 .2 (1110101.001)_{2}= (75.2)_{16}The equivalent hexadecimal value for the binary(1010111)_{2}is (57)_{16}