created: 07/15/2015; improved 04/10/16; improved again 04/22/23

The algorithm is:

number = positive integer ; bitstring = "" while (number > 0 ) { bit = number mod 2 ; append bit to the left of bitstring; quotient = number div 2 ; number = quotient ; } mod means remainder after integer division. div means quotient after integer division.

Positive Integer: | |
---|---|

Number: | |

bit = Number Mod Two | |

Bit String | |

quotient = Number Div Two | |

number = quotient |

**To start:** Enter a decimal representation of a not too big positive integer in the *Positive Integer* box.

**Then:** Click *Initialize* to assign the integer to *number*.

**Then:** Click *Divide by Two* to compute the quotient and remainder. The remainder will be 0 or 1. That bit is copied to the left of the bit string.

**Click** *Repeat* to go through the cycle again. Quit when the number has been reduced to zero.

The algorithm is:

number = decimal fraction ; bitstring = "." while ( number > 0 ) { number = number * 2 ; bit = 1 or 0 left of the decimal point ; append bit to the right of bitstring ; number = digits right of the decimal point ; }

Positive Decimal Fraction: | |
---|---|

Number: | |

Number = Number * 2 | |

bit = bit in 1's place | |

bit String = bit String + bit | |

number = digits right of point |

**To start:** Enter a decimal representation of a fraction in the *Positive Decimal Fraction* box.

**Then:** Click *Initialize* to assign the fraction to *number*.

**Then:** Click *Multiply by Two* . A bit will appear in the 1's place. That bit will be 0 or 1. Copy it to the right of the bit string.

**Click** *Repeat* to go through the cycle again. Quit when the fraction is zero or you have enough bits.