Do you know? How to do** decimal to binary conversion**? If not? Then let me explain to you, how to do that?

We can write a decimal number suppose 6825.8 and can be represented like this

6000+800+20+5+0.8 =6825.8

Also, we can write 6825.8 as where 10 is called **base**

#### The position values for decimal number are power’s of 10

There are two methods by which you can do decimal to binary conversion

#### First method

**Find the decimal to the binary conversion of 13**

Divide the value 13 by 2 till you get 0 or 1 as a remainder

**Conversion step’s**

**First**: divide the value 13 with value 2 and the remainder will be 1

13 2 =6 and remainder is 1

**Second**: divide the 6 with 2 and the remainder will be 0

6 2=3 and the remainder is 0

**Third**: divide the 3 with 2 and the remainder will be 1

3 2=1 and the remainder is 1

Write down all the remainder values from downward’s to upward

A binary value of 13 is 1101

#### Binary to Decimal conversion

find the binary to the decimal conversion of 1101

A decimal value of 1101 is 13

**Convert the decimal number 0.128906211 into a binary equivalent number**

**Conversion step’s**

**first**: multiply the fraction decimal number 0.128906211 with 2 the result will be 0.257812422

write the first digit of 0.257812422 as recorded carries 0

**second**: multiply the fraction decimal number 0.257812422 with 2 the result will be 0.515624844

write the first digit of 0.515624844 as recorded carries 0

**third**: multiply the fraction decimal number 0.515624844 with 2 the result will be 1.031249688

write the first digit of 1.031249688 as recorded carries 1

**fourth**: multiply the fraction decimal number 0.031249688 with 2 the result will be 0.062499376

write the first digit of 0.062499376 as recorded carries 0

**fifth**: multiply the fraction decimal number 0.062499376 with 2 the result will be 0.124998752

write the first digit of 0.124998752 as recorded carries 0

**sixth**: multiply the fraction decimal number 0.124998752 with 2 the result will be 0.249997504

write the first digit of 0.249997504 as recorded carries 0

**seven**: multiply the fraction decimal number 0.249997504 with 2 the result will be 0.499995008

write the first digit of 0.499995008 as recorded carries 0

**eight**: multiply the fraction decimal number 0.499995008 with 2 the result will be 0.999990016

write the first digit of 0.499995008 as recorded carries

write down the recorded carries values from upward to downward

the binary value of 0.128906211 is 0.00100001

**as you can note**: the fractional values of decimal number 0.128906211 are continuous in nature because of that, I just took only 8 fractional values which made the result as an **approximate result**

the **accurate result** can be acquired by continuously multiplying by 2 until we get many digits

**Convert decimal number 0.7412 to its binary equivalent**

Multiply the value 0.7412 by 2 till you get the 0 and record carries in that process

As you can notice the fractional values are continuous so that I just took 20 fractional values,It is an approximate value

if we want accurate value then we need to continue to multiply by 2 till we have many digits

A binary value of 0.7412 is 0.10111101101111110101

**Find the decimal to the binary conversion of 6825.3666**

**Step 1**: separate the integer part and fractional part

Integer part: 6825 fractional part:0.3666

**Step 2**: find the binary equivalent for the integer part

A binary value of 6825 is 1101010101001

**Step 3**: Find the binary equivalent for the fractional part

The binary value of 0.3666 is **approximate value** as I took only 17 fractional values to get the accurate value you need to continually multiple by 2 till you get multiple values

The binary value of 0.3666 is 0.01011101110110011

**Step 4**: combine the binary equivalent of integer and the fractional part

A binary value of 6825.3666 is 1101010101001.01011101110110011

#### Second method

**Find the binary equivalent of decimal 13**

**Step1** : Select the nearest of 13 or less than 13 value from the above table

The nearest value of 13 is 8 so, keep in place of 8 as 1

**Step2**: subtract the value 8 with 13

13-8 =5

**Step3** : Select the nearest of 5 or less than 5 value from the above table

The nearest value of 5 is 4 so, keep in place of 4 as 1

**Step4**: subtract the value 5 with 4

5-4 =1

**Step5** : Select the nearest of 1 or less than 1 value from the above table

The nearest value of 1 is 1 so, keep in place of 1 as 1

**Step6:** subtract the value 1 with 1

1-1 =0

If you get 0 value at the end then you need to finish the process and apply zero value to the remaining elements

The binary value of 13 is 1101

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