Decimal to Binary Converter
to Convert Base 10 to Base 2

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The Decimal to Binary Converter on this page will convert base 10 numbers to base 2 numbers, and show its work.

This free online decimal to binary calculator will convert decimal numbers into binary numbers and display a conversion chart to show how it formulated the result.

If you're not sure what a binary number is, or you wish to convert from base 2 to base 10 instead of the other way around, please visit the Base 2 to Base 10 Conversion Calculator.

What is a Decimal Number?

As it relates to the conversion calculator on this page, a decimal number is a numerical expression that uses the base 10 system for counting and representing values. Of course, this base 10 system -- which uses the numbers 0 through 9 -- is the number system most of us were taught from toddler age on. In fact, the reason we don't add a subscripted 10 to base 10 numbers, is because we know it will just be assumed. This can't be said for the other bases.

Aside from the numbers used, the base 10 system assigns a power of 10 to each place value, like this:

Place Values of Base 10 System

Power of 10: 103 102 101 100 . 10-1 10-2 10-3
Place value : 1000 100 10 1 . 1/10 1/100 1/1000

Now, since we are looking to convert a base 10 number into a base 2 number, let's compare the above with the place values in a binary number system, which only uses the number 0 and 1:

Place Values of Base 2 System

Power of 2: 23 22 21 20 . 2-1 2-2 2-3
Place value : 8 4 2 1 . 1/2 1/4 1/8

So you see, since each place value in a base 10 number is different than the corresponding place value in a base 2 system, we need a method for converting 0-9 base 10 place values into 0-1 base 2 place values.

How to Convert Decimal to Binary

In order to convert a base 10 number into a base 2 number, the first step is to find the first base 2 place value that is greater than or equal to the decimal number you are converting -- starting at the 20 place and working your way to the left. For example, suppose you want to convert the decimal number 15 into a binary number. In that case you would find the first base 2 place value that is greater than or equal to 15, which would be 16:

First Base 2 Value Greater than 1510

Power of 2: 24 23 22 21 20
Place value : 16 8 4 2 1

Once you have located your base 2 place value starting point, the next step is to create a conversion chart, like this:

Conversion Chart

A Power of 2: 24 23 22 21 20
B Remainder of Division: 15        
C Place value (A result): 16 8 4 2 1
D Binary digit  B ÷ C:          

Notice that the decimal you want to convert is placed in left-most cell of Row B, just above the base 2 place value row (C).

Next, attempt to divide the amount in row B into the amount in row C. If the amount in row C is greater than the amount in row B, enter a "0" in row D and move the amount in row B one cell to the right. Otherwise, if the amount in row C is less than the amount in row B, enter a "1" in row D and enter the difference between B and C (remainder) in the next open cell in row B. Then simply repeat this process for each subsequent column, like this:

Conversion Chart for Converting 1510 to Binary

A Power of 2: 24 23 22 21 20
B Remainder of Division: 15 15 7 3 1
C Place value (A result): 16 8 4 2 1
D Binary digit  B ÷ C: 0 1 1 1 1

Divide each cell in row C into the corresponding cell in row B and move the remainder of each division to the next cell in row B. Repeat for all columns. Note that the above is how the decimal to binary converter will show its work.

From the above we can see that the base 10 number 15 converts to the base 2 number 1111 (one-one-one-one). Note that the leading zeros are dropped since they represent no value (just like the base 10 system).

As you can see, converting a decimal number to a binary number is a simple process of identifying the first base 2 place value greater than or equal to the base 10 number you are converting, and then dividing each place value into the remainder of previous division.

With that, let's use the Decimal to Binary Converter to convert base 10 to base 2.

Decimal to Binary Converter
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Instructions: Enter the decimal number you would like to convert into a binary number, and then click the "Convert Decimal to Binary" button.

Mouse over the blue question marks for a further explanation of each entry field. More in-depth explanations can be found in the glossary of terms located beneath the Decimal to Binary Converter.

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Help Binary (base 2) equivalent: 2
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Decimal to Binary Converter Glossary of Terms

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Binary system: Number system that uses the base 2 system of expressing values, which consist only of the digits 0 and 1. Base 2 numbers are usually written with a subscripted 2 behind them (10102). The binary system is what electronic devices use for counting and displaying information, as their internal switches recognize a 0 as "off" and a 1 as "on." Each digit within a base 2 number is called a "bit" (comes from binary digit).

Decimal (base 10) number: Enter the decimal (base 10) number you would like to convert into a binary number. Note that the entered number may only consist of digits 0-9, a single decimal point, and the leading number must not be a zero. For numbers containing a decimal point, the decimal to binary converter will only convert out to the last digit entered.

Binary (base 2) equivalent: This is the binary equivalent to the entered decimal number. Note that if the result ends with 3 dots, it means either the result is incomplete or it is a repeating decimal. Also note that after clicking the Convert Decimal to Binary button the Decimal to Binary converter will display a detailed explanation of how it arrived at the result immediately below this line.

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