Decimal to Binary Conversion (with Fractional Part)

In this article, we will learn how to convert a number from the decimal system to the binary system, and we will also look at an example. But before we get started, let's make sure we're clear on what these two numbers represent.

Decimal to Binary Conversion with an Example

Any decimal number can be converted into a binary number by dividing the decimal number by the base of the binary number system, which is 2. Let's look at an example of this conversion's working rule so that we can get a better understanding of it.

Now that we have a number in the decimal number system, let's say 105, our task is to find that number or one that is equivalent to it in binary form or in the binary number system. Let's focus on the information presented in the following figure:

decimal to binary number

From the above figure, we will get 1101001, which is the same number as 105, but in the binary number system. Therefore, (105)10 = (1101001)2.

Decimal (containing a fractional part) to Binary Conversion Steps

Here are the steps or rules of multiplication for fractional part conversion:

Let’s take an example to apply the above steps practically and learn how we can convert any fractional part value given in the decimal number system to the binary version of the same fractional part.

In this case,.42 must be converted to binary. That is, (.42)10 = ( ? )2.

The table given below shows the step-by-step multiplication of the fractional part as directed in the above rules.

Decimal Fractional Multiply with Base Multiplication Result Carry Value
.42 * 2 0.84 0 MSB
.84 * 2 1.68 1
.68 * 2 1.36 1
.36 * 2 0.72 0
.72 * 2 1.44 1 LSB

As you can see, the multiplication procedure

As a result, this is equivalent to .42, which is 0.01101. Or, (0.42)10 = (0.01101)2.

Programs Created on Decimal to Binary Conversion

Computer Fundamentals Quiz

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