Binary to Decimal Converter to Convert Base 2 to Base 10

Binary to Decimal Converter Sign

This calculator will convert binary numbers into decimal 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 how to manually convert one into a decimal, it may help to visit the Learn tab before using the calculator.

Note that if you are looking to convert a base 10 number to a base 2 number, please visit the Decimal To Binary Converter.

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Binary to Decimal Converter

Convert binary to decimal number and create the conversion chart.

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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
Binary number:Binary number:Binary number (base 2):Binary number (base 2):

Binary number (base 2):

Enter the binary number you would like to convert into a decimal number. Note that the entered number may only consist of ones, zeros, and a single decimal point, and the leading number must not be a zero.

Decimal:Decimal:Decimal (base 10):Equivalent decimal (base 10):

Decimal (base 10) equivalent:

This is the decimal equivalent to the entered binary number. Note that after clicking the Convert Binary to Decimal button the binary to decimal 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.

Help and Tools

Learn

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

What is a Binary Number?

A binary number is a number that consists of only 1s and 0s. Binary numbers use the base 2 system (hence the "bi" in binary), as opposed to decimal numbers that use the base 10 system.

In other words, the decimal system (base 10) uses only the digits 0,1,2,3,4,5,6,7,8 and 9, whereas the binary system (base 2) uses only the digits 0 and 1.

To differentiate between a base 2 and a base 10 number, base 2 numbers are usually written with a 2 as the subscript. For example, 1012 would tell you that the number is the binary number one-zero-one, and not the decimal number one-hundred-one.

How to Convert Binary to Decimal

To help you to understand how to convert binary to decimal, it may help to look at how we translate the value of a decimal number. Let's use the decimal number 1234 (123410, or one-thousand, two-hundred and thirty-four) as an example:

Translating the Value of a Decimal (base 10) Number

← swipe left and right →← swipe left and right →
APower of 10:103102101100
BPlace value (A result):1000100101
CEntered decimal digit:1234
DProduct of B * C:1000200304
ECumulative total of D:1000120012301234

With the above base 10 translation in mind, here is how you would convert the base 2 number 1111 (11112 or one-one-one-one) into a base 10 number:

Converting a Binary (base 2) to a Decimal (base 10)

← swipe left and right →← swipe left and right →
APower of 2:23222120
BPlace value (A result):8421
CEntered binary digit:1111
DProduct of B * C:8421
ECumulative total of D:8121415

Adding the values of line D we get the base 10 number of 15. In other words, the number 11112 coverts to the number 1510.

As you can see, converting a binary number to a decimal number is a simple process of identifying the place value of each digit, multiplying each digit by its place value, and then adding up all of the products.

Converting Base 2 Numbers That Have Decimal Points

If the base 2 you want to convert has a decimal point in it, you simply continue subtracting 1 from each exponent (line A below) as you move from left to right. For example, here is how you would convert 111.1012 into its base 10 equivalent:

Converting a Binary That Has a Decimal Point

← swipe left and right →← swipe left and right →
APower of 2:2221202-12-22-3
BPlace value (A result):4210.50.250.125
CEntered binary digit:111101
DProduct of B * C:4210.500.125
ECumulative total of D:4677.57.57.625

Adding the values of line D we get the decimal number 7.625. In other words, the number 111.1012 coverts to the number 7.62510. Note that the red exponents in line A indicate digits that are located to the right of the decimal point.

So you see, in a binary number each place value to the right of the decimal point decreases by 1/2 (--> 1/2, 1/4, 1/8, etc.) as opposed to the place values to the left of the decimal point whose values double with each place you move to the left (8, 4, 2, 1 <--).

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.