Converter Calculator

Welcome to our Online Binary-Decimal Converterr.

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

The calculator will also take you through all the working out step-by-step along the way.

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

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.

1) Convert 10110 from binary to decimal.

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

2^{4} |
2^{3} |
2^{2} |
2^{1} |
2^{0} |
---|---|---|---|---|

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.

2^{6} |
2^{5} |
2^{4} |
2^{3} |
2^{2} |
2^{1} |
2^{0} |
---|---|---|---|---|---|---|

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

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.

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 = 2^{3} + 2^{2} + 2^{0}

Step 2) We write binary place value grid out using powers of 2 up to 2^{3} which is the largest.

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

2^{3} |
2^{2} |
2^{1} |
2^{0} |
---|---|---|---|

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:

2^{3} |
2^{2} |
2^{1} |
2^{0} |
---|---|---|---|

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 = 2^{5} + 2^{3} + 2^{2}

Step 2) We write binary place value grid out using powers of 2 up to 2^{5} which is the largest.

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

2^{5} |
2^{4} |
2^{3} |
2^{2} |
2^{1} |
2^{0} |
---|---|---|---|---|---|

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:

2^{5} |
2^{4} |
2^{3} |
2^{2} |
2^{1} |
2^{0} |
---|---|---|---|---|---|

32 | 16 | 8 | 4 | 2 | 1 |

1 | 0 | 1 | 1 | 0 | 0 |

So 44 = 101100 in binary.

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

Binary | Decimal |
---|---|

0000 | 0 |

0001 | 1 |

0010 | 2 |

0011 | 3 |

0100 | 4 |

0101 | 5 |

0110 | 6 |

0111 | 7 |

1000 | 8 |

1001 | 9 |

1010 | 10 |

1011 | 11 |

1100 | 12 |

1101 | 13 |

1110 | 14 |

1111 | 15 |

Take a look at some more of our resources similar to our mm to inches conversion calculator.

Our number system converters will convert numbers from binary, octal or hexadecimal into decimal (or from decimal to binary, octal or hex).

The calculators also show you detailed working out so you can see how to do it yourself!

Our prime number calculator will help you to find all the factors of any given number and tell you whether or not the number you are looking at is prime or not.

The calculator will also show you your number as a product of primes.

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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