Online Binary-Decimal
Converter Calculator

Welcome to our Online Binary-Decimal Converterr.

This converter will convert binary numbers to decimal, or decimal numbers to binary.

Online Binary-Decimal Converter

binary to decimal converter

binary

    Answer   

decimal

 
 
   


How It Works

Here is our binary to decimal conversion calculator which will help you convert between the two different bases of number systems.

The converter will also show you the formula you need to convert between units.

Online Binary-Decimal Converter - How It Works...

Step 1) Choose which calculator you want - binary to decimal or decimal to binary

Step 2) Type in the number you want to convert.

Step 3) Click the Convert button and the answer will be displayed.


How to convert binary to decimal

How to convert binary to decimal

To convert a binary number (base-2) to the decimal (base-10) number system, we need to use binary place value to add the decimal value of each digit.

Each time you move a place to the left, the value increases two-fold.


Examples

1) Convert 10110 from binary to decimal.

Step 1) Write down the place value of each digit.

24 23 22 21 20
16 8 4 2 1
1 0 1 1 0

Step 2) Add up the place value of each digit.

16x1 + 8x0 + 4x1 + 2x1 + 1x0

= 16 + 4 + 2 = 22

So 10110 in binary is equal to 22.



2) Convert 1011011 from binary into decimal.

Step 1) Write down the place value of each digit.

26 25 24 23 22 21 20
64 32 16 8 4 2 1
1 0 1 1 0 1 1

Step 2) Add up the place value of each digit.

64x1 + 32x0 + 16x1 + 8x1 + 4x0 + 2x1 + 1x1

64 + 16 + 8 + 2 + 1 = 91

So 1011011 in binary is equal to 91.

How to convert decimal to binary

How to convert decimal to binary

To convert a decimal number (base-10) to the binary (base-2) number system, we need to use rewrite the decimal number as a sum of powers of 2.

The powers of 2 are then converted to 1s in the binary place value and zeroes used as placeholders.


Online Binary-Decimal Converter Worked Examples

Example 1) Convert 13 from decimal to binary.

Step 1) Rewrite the number as a sum of powers of 2.

The powers of 2 are 1, 2, 4, 8, 16, 32, 64, ...

So 13 = 8 + 4 + 1

Or we could say that 13 = 23 + 22 + 20

Step 2) We write binary place value grid out using powers of 2 up to 23 which is the largest.

Each power of 2 we have is represented as a one giving us:

23 22 21 20
8 4 2 1
1 1   1

All we need to do now is to fill in the blank numbers with zeroes.

This gives us:

23 22 21 20
8 4 2 1
1 1 0 1

So 13 = 1101 in binary.



Example 2) Convert 44 from decimal to binary.

Step 1) Rewrite the number as a sum of powers of 2.

The powers of 2 are 1, 2, 4, 8, 16, 32, 64, ...

So 44 = 32 + 8 + 4

Or we could say that 44 = 25 + 23 + 22

Step 2) We write binary place value grid out using powers of 2 up to 25 which is the largest.

Each power of 2 we have is represented as a one giving us:

25 24 23 22 21 20
32 16 8 4 2 1
1   1 1    

All we need to do now is to fill in the blank numbers with zeroes.

This gives us:

25 24 23 22 21 20
32 16 8 4 2 1
1 0 1 1 0 0

So 44 = 101100 in binary.

Online Binary-Decimal Converter Quick Table

This quick conversion table converts binary numbers up to the value of 15 into decimal.

Binary Decimal
00000
00011
00102
00113
01004
01015
01106
01117
10008
10019
101010
101111
110012
110113
111014
111115

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Need to Learn More about Binary Numbers

If you want to learn more about binary numbers, take a look at this article in the kiddle encyclopedia!

The article talks about the history of binary numbers, binary arithmetic and has some other facts too!

Using the link below will open the kiddle webpage in a new browser window.

 

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