# Base conversions

From WikiEducator

## Converting from any other base to base 10.

To convert from any base to to base 10 can be broken down into 3 simple steps.

- First put the place value of each binary digit
- Second, Multiply each place value by its corresponding digit
- Add the products that you got from multiplying in step two

Converting 11101_{2} to base 10

Step 1 (since we are converting from base 2, Put the place values for base 2)

place values | 16 | 8 | 4 | 2 | 1 |
---|---|---|---|---|---|

Digits | 1 | 1 | 1 | 0 | 1 |

Step 2 (Multiplying the place value by the corresponding digit to get the products)

place values | 16 | 8 | 4 | 2 | 1 |
---|---|---|---|---|---|

Digits | 1 | 1 | 1 | 0 | 1 |

Products | 16 | 8 | 4 | 0 | 1 |

Step 3 (Add the products together)
16 + 8 + 4 + 0 + 1 = 29_{10}

Converting 142_{8} to base 10

Step 1 (since we are converting from base 8, Put the place values for base 8)

place values | 64 | 8 | 1 |
---|---|---|---|

Digits | 1 | 4 | 2 |

Step 2 (Multiplying the place value by the corresponding digit to get the products)

place values | 64 | 8 | 1 |
---|---|---|---|

Digits | 1 | 4 | 2 |

Products | 64 | 32 | 2 |

Step 3 (Add the products together)
64 + 32 + 2 = 98_{10}