In this page we will learn about decimal to binary conversion. Binary number is number with base 2 and decimal number is a number with base 10.This conversion is very important because in computers the data is stored in binary format.and the user enters the number in decimal format so system will convert decimal to binary and store it. Let us see what is a binary number and decimal number and conversion of decimal to binary.

**Binary numbers:**

Binary refers to characterized by or consisting of two parts or components. The word binary denotes two (sections or subjects or values). The binary value in mathematics is having only two values 0s and 1s. The number which is expressed only in 0s and 1s are called binary numbers. The binary numbers are represented as that of decimal numbers. The numbers are placed left or right of the point. The numbers may be greater than one or less than one.

**Decimal numbers:**

Decimal number is a number which is formed with combination of two parts.one part is called integer part and other part is called fractional part.part which exist left of decimal point is called integer part and part right of decimal point is called fractional part.

For example : 5.36

here 5 = integer part

36 = fractional part

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Below are the steps for how to convert decimal to binary number -

**Step 1:** Divide given number starting from 2 as suitable.

**Step**** ****2: **Write remainder on the right side of quotient.

**Step**** 3: **Divide untill quotient will be 0.

**Step**** 4: **Now write binary number starting from lower end of that divison.

**Step**** 5: **Now write given number including quotient of lower end.that should be starting point.

Below are the problems based on converting decimal to binary -

The binary number can be calculated by using L division method

2 | 35

-------

2 | 17 -- 1

-------

2 | 8 -- 1

-------

2 | 4 --0

-------

2 | 2 -- 0

--------

1 -- 0

The binary number can be calculated by using L division method

2 | 65

-------

2 | 32 -- 1

-------

2 |16 -- 0

-------

2 | 8 --0

-------

2 | 4 -- 0

--------

2 |__ 2 -__- 0

1

The binary number can be calculated by using L division method

2 | 142

-------

2 | 71 -- 0

-------

2 | 35 -- 1

-------

2 | 17 -- 1

-------

2 | 8 -- 1

--------

2 | 4 -- 0

---------

2 | 2 -- 0

----------

1 -- 0

From the above conversion, we divide the given decimal number by the base (2) and get the remainder. Then the remainders all are considered from bottom to top to get the binary value of the decimal number.This way, we can convert the decimal to binary.

Binary number is 01100.011.

01100.011 =(0 x 2^{4}) + (1 x 2^{3}) + (1 x 2^{2}) + (0 x 2^{1}) + (0 x 2^{0}) + (0 x `1/ 2` ) + (1 x `1/2^2` ) + (1 x `1/2^3` )

= 0 + (1 x 8) + (1 x 4) + 0 + 0 + 0 + 0.25 + 0.125

= 8 + 4 + 0.25 + 0.125

= 12 + 0.375

= 12.375

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