# Decimal to Binary Converter to Convert Base 10 to Base 2 This calculator will convert decimal numbers into binary numbers and display an interactive conversion chart to show how it arrived at the result.

Tapping any number within the generated conversion chart will display an explanation of how the calculator arrived at the number located within the tapped cell.

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.

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## Decimal to Binary Converter

Convert decimal to binary number and create the conversion chart.

Special Instructions

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#### Selected Data Record:

A Data Record is a set of calculator entries that are stored in your web browser's Local Storage. If a Data Record is currently selected in the "Data" tab, this line will list the name you gave to that data record. If no data record is selected, or you have no entries stored for this calculator, the line will display "None".

DataData recordData recordSelected data record: None
Decimal:Decimal number:Decimal number (base 10):Decimal number (base 10):

#### Decimal number (base 10):

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.

 # Decimal number
Binary:Binary:Binary (base 2):Equivalent binary (base 2):

#### 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.

If you would like to save the current entries to the secure online database, tap or click on the Data tab, select "New Data Record", give the data record a name, then tap or click the Save button. To save changes to previously saved entries, simply tap the Save button. Please select and "Clear" any data records you no longer need.

## Learn

### What a decimal number is and how to convert it to a binary number.

#### 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

← swipe left and right →← swipe left and right →
 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

← swipe left and right →← swipe left and right →
 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

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

← swipe left and right →← swipe left and right →
 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

← swipe left and right →← swipe left and right →
 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:

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:

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

Conversion Chart for Converting 1510 to Binary

← swipe left and right →← swipe left and right →
 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.

#### Adjust Calculator Width:

Move the slider to left and right to adjust the calculator width. Note that the Help and Tools panel will be hidden when the calculator is too wide to fit both on the screen. Moving the slider to the left will bring the instructions and tools panel back into view.

Also note that some calculators will reformat to accommodate the screen size as you make the calculator wider or narrower. If the calculator is narrow, columns of entry rows will be converted to a vertical entry form, whereas a wider calculator will display columns of entry rows, and the entry fields will be smaller in size ... since they will not need to be "thumb friendly".

#### Show/Hide Popup Keypads:

Select Show or Hide to show or hide the popup keypad icons located next to numeric entry fields. These are generally only needed for mobile devices that don't have decimal points in their numeric keypads. So if you are on a desktop, you may find the calculator to be more user-friendly and less cluttered without them.

#### Stick/Unstick Tools:

Select Stick or Unstick to stick or unstick the help and tools panel. Selecting "Stick" will keep the panel in view while scrolling the calculator vertically. If you find that annoying, select "Unstick" to keep the panel in a stationary position.

If the tools panel becomes "Unstuck" on its own, try clicking "Unstick" and then "Stick" to re-stick the panel.