 # Decimal to Binary Converter

Enter decimal number and click calculate button to convert that number from decimal to binary

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## Decimal to Binary Converter

The decimal-to-binary converter is a tool designed to change values from the decimal system to the binary system.

This tool converts the “decimal numbers”, the ones which contain a decimal point from the “Decimal numbering system” (`base 10 system`) to their equivalent

It also provides the 2’s complement if it is available for a number.

## How to use this tool?

To use the decimal-to-binary converter, follow the steps given below.

1. Enter the decimal number or any simple number from the base 10 system.
2. Select the “digit grouping” to get the answer in bytes (`8-bit grouping`).
3. Click on “Calculate”.

## What is a binary number system?

Computers only understand the binary number system due to their basic architecture. As its name suggests, binary is a base-2 system and uses only two digits - 0 and 1

The logic underpinning the binary is quite simple. The binary digit 0 typically represents an 'off' state, while 1 represents an 'on' state in digital electronics.

## What is a decimal number system?

On the other hand, we humans are accustomed to using a decimal system or base-10 system. This system uses ten digits that include all the numbers between 0 to 9.

Within the decimal system, decimal numbers are such numbers that consist of two parts; a whole and a fraction. Such “7.8”. The digit 7 is a whole number and .8 is the fraction part of it.

## How to convert numbers from decimal to binary system?

Converting decimal numbers to binary might seem complex, but it is quite straightforward once you understand the method. The process can be summarized in a few steps:

1. Divide the decimal number by 2.
2. Note the remainder.
3. Divide the quotient from the previous step by 2.
4. Again, note the remainder.
5. Repeat the process until the quotient is 0.

The binary equivalent is the sequence of remainders in reverse order.

### Example:

Convert the decimal number 13 into binary.

 Divided by 2 result remainder Binary value 13/2 6 1 1 6/2 3 0 0 3/2 1 1 0 1/2 0 1 1

Thus, the binary equivalent of decimal `13 is 1101`.

## How to convert “decimal numbers” from decimal to binary system?

Decimal to binary conversion of a number containing a decimal point involves converting both the whole number and the fractional parts separately.

### Example:

Convert 10.625 to binary.

Step 1: Convert the Whole Number Part.

To convert the integer part (`10 in this case`), follow the same process as outlined in previous examples:

 Divided by 2 result remainder Binary value 10/2 5 0 0 5/2 2 1 1 2/2 1 0 0 1/2 0 1 1

Reading the remainder from bottom to top gives 1010, which is the binary representation of the decimal number 10.

Step 2: Convert the Fractional Part.

To convert the fractional part (`0.625 in this case`), multiply by 2, and keep track of the whole numbers:

 Divided by 2 result remainder Binary value 0.625/2 1.35 1 1 0.25/2 0.5 0 0 0.5/2 1.0 1 1

The process stops when you reach a product of 1.0 or when the fraction becomes 0. Take the whole numbers in the order they're produced, giving 101 for the fractional part.

Step 3: Combine the Two Parts.

Finally, combine the whole number part and the fractional part, using a binary point (analogous to the decimal point in decimal numbers) to separate them. So, the binary representation of` 10.625 is 1010.101`.

This process works for any decimal number with a fractional part. Just remember that for fractions, the process either stops when you reach a product of 1.0 or the fraction becomes 0, or you choose to stop at a certain level of precision.

## What is digit grouping?

In the context of decimal-to-binary conversion, digit grouping usually refers to grouping binary digits (bits) in sets of a certain size for easier readability and interpretation.

The most common grouping in binary is 8 bits, which forms a byte. A byte can represent a decimal number from `0 to 255` or two hexadecimal digits from `00 to FF`. For example, the binary number 1101 0101 forms a byte, representing the decimal number 213 or the hexadecimal number D5.

Grouping binary digits can make long binary numbers easier to read and can make conversions between binary, decimal, and hexadecimal more manageable.

In computing, these groupings also often align with how data is structured and processed, with bytes being the most fundamental unit of data in many systems.

Let’s solve another example to illustrate the byte grouping.

### Example:

Convert the decimal number 432 into binary:

 Divided by 2 result remainder Binary value 432/2 216 0 0 216/2 108 0 0 108/2 54 0 0 54/2 27 0 0 27/2 13 1 1 13/2 6 1 1 6/2 3 0 0 3/2 1 1 1 1/2 0 1 1

The binary equivalent of `432 is 110110000`. However, for grouping by bytes (8 bits), it should be presented as 00000001 10110000, adding leading zeros to ensure the binary number fills an entire byte.

## What is the importance of decimal-to-binary conversion?

It is often necessary to convert decimal numbers to binary and vice versa, especially in computer science and digital electronics. For instance, to know how a specific decimal number is represented in binary inside a computer, we need to perform a decimal-to-binary conversion.

Another instance is subnetting in computer networks. Subnetting is a practice that divides a network into two or more networks, and it is often done using binary numbers.

Network engineers often have to convert IP addresses, which are typically written in decimal, into binary for subnetting calculations.

## Decimal to binary table:

 Decimal Binary 5 00000101 18.5 00010010.1 7 00000111 32.25 00100000.01 11 00001011 26.5 00011010.1 15 00001111 19.75 00010011.11 8 00001000 29.375 00011101.011 4 00000100 23.625 00010111.101 10 00001010 13.5 00001101.1 21 00010101 31.875 00011111.111 2 00000010 17.25 00010001.01 9 00001001 27.125 00011011.001

Note: The fractional binary values are not commonly used directly in many computing systems, as most systems operate on whole binary numbers.

However, understanding how fractional binary values work can be important for understanding concepts like fixed-point and floating-point representation, which are used to represent non-integer numbers in digital systems.

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