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Table of Contents

Binary to decimal converter does what we always wanted to do in seconds. It helps in converting binary to decimal in a blink of an eye. Using binary to decimal converter, the conversion of binary to number (base-2 to base-10) is an important concept to understand as the binary numbering system forms the basis for all computers and digital systems.

In binary to base 10, the Base-of-10 numbering system is called the decimal or "denary" counting system where each digit in a number assumes one of ten possible values, called "digits," from 0 to 9, e.g. 213_{10} (Twenty-first hundred).

But as well as having 10 digits (0 through 9), the decimal numbering system also has addition, subtraction, multiplication, and division.

Each digit has a value ten times higher than its previous number in a decimal system and this decimal numbering system uses a set of symbols, **b**, together with a base, **q**, to determine the weight of each digit within a number. The six in sixty, for example, have a lower weight than the six in six hundred.

**N= b _{i}q^{i}**

*Where:* **N** is a real positive number

**b** is the digit

**q** is the base value

and integer (i) can be positive, negative or zero

N = b

_{n}q^{n}… b_{3}q^{3}+ b_{2}q^{2}+ b_{1}q^{1}+ b_{0}q^{0}+ b_{-1}q^{-1}+ b_{-2}q^{-2}… etc.

Each integer number column has unit values, tens, hundreds, thousands, etc. in the decimal, base-10 (den) or denary numbering system as we move along the number from right to left. These values are written mathematically as **10 ^{0}, 10^{1}, 10^{2}, 10^{3}** etc. Then each position on the left of the decimal point indicates an increase of 10. Similarly, the weight of the number becomes more negative for fractional numbers as we move from left to right,

The binary to decimal conversion can be performed by plotting each binary digit value corresponding to its decimal digit value in each column or using binary number converter. Each column is an exponent's number 2. The exponent grows from right to left by one. You can add the value of those columns tagged as ON or equivalent to 1 to get the total value.

For example, the 101100101 binary number is converted as follows to a decimal number:

Exponent = 2

^{8}2^{7}2^{6}2^{5}2^{4}2^{3}2^{2}2^{1}2^{0}

**Total value =** (256+64+32+4+1) = 357

*So the binary number 101100101 is 357 in decimal numbers.*

Binary to decimal calculator converts binary to integers and make it easy for binary decimal users.

What else we have to offer than bin to dec? We have developed advanced binary conversion tools like hex to decimal converter, decimal to hex converter, Binary Translator, text to binary converter and **decimal to binary converter**. Now it’s not tough to convert different number systems into each other as we offer multiple conversion tools for this purpose.

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 |

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