# Converting binary to decimal

Given the binary value 1000:

*1000*

*= 1 * 2 ^{3} + 0 * 2² + 0 * 2^{1} + 0 * 2^{0}*

*= 2*

^{3}*= 8 (decimal)*

# Converting decimal to binary

Given the decimal value 10:

*10*

*= 2 ^{3} + 2^{1}*

*= 1 * 2*

^{3}+ 0 * 2^{2}+ 1 * 2^{1}+ 0 * 2^{0}*= 1010 (binary)*

An easier way to work this out is, for example, given a decimal number of 11:

- divide the decimal number by 2, recording the quotient and remainder in the next row
- rounding the quotient DOWN each time, until you have a quotient of 0.

Quotient | Remainder | ||
---|---|---|---|

11 | |||

Repeat the procedure - divide by 2, record quotient and remainder in the next row | 5 | 1 | 11/2 = 5 remainder 1 |

Repeat again | 2 | 1 | 5/2 = 2 remainder 1 |

Repeat again | 1 | 0 | 2/2 = 1 remainder 0 |

Stop! Quotient = zero | 0 | 1 | 1/2 = 0 remainder 1 |

**Result:** (read from bottom up) Decimal value 11 = binary 1011