Converting binary to decimal is a common task in computer programming. Binary is a `base-2`

number system that uses only two digits, 0 and 1. Decimal, on the other hand, is a `base-10`

number system that uses ten digits, 0 through 9. Converting binary to decimal involves multiplying each digit of the binary number by its corresponding power of 2 and adding up the results.

## Conversion

Here’s a step-by-step guide on how to convert binary to decimal:

- Choose the binary number you want to convert to decimal.
- Write down the powers of 2 from right to left, starting with $2^0$.
- Multiply each digit of the binary number by its corresponding power of 2.
- Add up the results from step 3 to get the decimal value.

## Example

Let’s walk through an example to illustrate the process. Suppose we want to convert the binary number `1011`

to decimal.

- The binary number we want to convert is 1011.
- The powers of 2 from right to left are $2^0$, $2^1$, $2^2$, and $2^3$
- We multiply each digit of the binary number by its corresponding power of 2. The results are: $1 \times 2^0 = 1$, $1 \times 2^1 = 2$, $0 \times 2^2 = 0$, and $1 \times 2^3 = 8$
- We add up the results from step 3 to get the decimal value. $1 + 2 + 0 + 8 = 11$ Therefore, the decimal value of the binary number 1011 is 11.

## Binary-Decimal Table

Here’s a table that shows the decimal values of the first 16 binary numbers:

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 |