Decimal to Binary

This website is all about decimal to binary. If you have asked yourself how to convert decimal numbers to binary then you have definitely come to the right place. To convert decimals to binary online, you most likely want to use a hassle-free tool. That is why you find our dec to bin converter right below, after a few words regarding the conversion. Also, we have a good number of examples and teach you the conversion method. Read on to learn all about decimal to binary.

Decimal to Binary Conversion

There are many reasons why you may need a decimal to binary conversion. Whereas the decimal (base ten) numeral system is made up of 10 possible values from 0 to 9, the binary (base two) numeral system only has the two values 0 and 1. If you are really into computing, then you probably want to learn about the conversion of decimal numbers to binary, as bits and bytes are represented in the binary system as zeroes and ones to the powers of two. The decimal binary conversion can easily be done manually, but once you got the hang of the conversion decimal to base 2 then you probably want to use our free tool below which does the conversion from automatically for you.

Decimal to Binary Converter

Here’s our decimal to binary converter which will do all work for you. To use the conversion calculator enter a decimal number or set the desired value using the arrows, then hit the convert button. You will then be shown the result in the binary number system. Either use the reset button or overwrite the existing number to continue using our converter online. Chances are high that you will need our converter again in the future so make sure to bookmark our site now as convert decimal to binary calculator.

Unsigned Signed

Decimal to Binary Conversion Method

Here we are going to show you how to convert decimals to binary. In fact, there is more than one. The first method is known as Short Division by Two with Remainder, whereas the second approach is called Descending Powers of Two and Subtraction.

Decimal to Binary Conversion Method 1

The first conversion method we are going to teach is called Short Division by Two with Remainder. We will teach it by example using the number 197 (base 10) and convert it to binary.
Decimal to Binary Conversion Method
1. We begin by writing the decimal number with a subscript of 10 to avoid confusion with the base 2 notation. It’s recommenced you use paper and pencil to reproduce the example. Write the decimal number 197 inside an upside-down long division symbol as dividend. Prepend the base of the destination system: 2.

2. We write the integer answer (quotient) under the long division symbol, and make a note of the remainder (0 or 1) to the right of the dividend. The remainder is always 0 or 1 because we are dividing by two.
Decimal to Binary Conversion Method Image
In our example the quotient is 98, and we have a remainder of 1.

3. Using the new quotient we repeat the above step until the quotient is 0.

Decimal to Binary Conversion Method Depiction

So, we divide 98 by 2 and write the remainder 1 to the right of 98. Then, we divide the quotient 49 by 2, and make note of the remainder 0. We continue this conversion method by dividing the quotient until we get 0 as the quotient.

4. Starting from the bottom we write down the remainders until we reach the top.
Decimal to Binary Conversion Method Representation

In our example the sequence is 11000101. 11000101 is the binary equivalent of the decimal number 197.

In subscript notation: 19710 = 110001012

We can check the result by building the sum of the powers of two, (disregarding the powers of 2 with zero as factor):

27 + 26 + 22 + 20 = 128 + 64 + 4 + 1 = 197

Converting from the decimal system to binary can also be done like this:

Decimal to Binary Conversion Method 2

Now let’s turn to the second conversion method known as Descending Powers of Two and Subtraction.

1. First, we create a chart with the powers of two from right to left, starting with 20, which equals one.
Decimal to Binary Conversion Method Illustration
Increase the exponent by 1 until you reach the number close to the decimal you are starting with. We again use 197 as the decimal number. Then we make a row using the numbers from the chart.

2. Start with the biggest number that will fit in the number you want to convert. In our example 128 is the greatest number that will fit into 197.
Decimal to Binary Conversion Method Figure
Write a 1 beneath your base 2 table’s leftmost binary digit. Next, subtract 128 from the decimal number you have started with. In our case of 197 the result is 69.

3. Move to the next lower power of two. If the number (result of previous subtraction) fits into write a 1, else a 0. In our example 64 fits goes into 69, so we write a 1 below it.
Decimal to Binary Conversion Method Drawing
We repeat the above and subtract 64 from 69. We now have 5. 5 goes into 4.

4. We keep on subtracting until we reach the end marking a 1 that goes into your new number.
Decimal to Binary Conversion Method Picture
Write a 0 beneath the numbers who don’t.

5. Write out the marked numbers from left to right as result of .
Decimal to Binary Conversion Method Visualization
The sequence of 1’s and 0’s you have is the binary equivalent of the integer(decimal) you have started with. In our example you should have: 11000101

Written with base subscripts: 19710 = 110001012

Proof: 27 + 26 + 22 + 20 = 128 + 64 + 4 + 1 = 197

Observation: The above methods for any number, regardless how many digit it has.

Now that you know all about converting decimals to binary keep using our conversion calculator above.

Decimal to Binary Conversion Examples

Now we show you a couple of conversion examples:

110 = 12
210 = 102
310 = 112
410 = 1002
510 = 1012
610 = 1102
710 = 1112
810 = 10002
910 = 10012
1010 = 10102

You can always check if an example is correct by summing the powers of two.

Finally, some more conversion examples:

2010 = 101002
5010 = 1100102
10010 = 11001002
100010 = 11111010002
1000010 = 100111000100002

If you are happy with our content please give us a Like or hit the share button. Also, we appreciate any feedback you might have. Also, you may also be interested in Meters to Miles, our length converter.

More information:

Leave a Reply

Your email address will not be published. Required fields are marked *

*


*

Search Conversions

Categories