Many of my articles address common topics; I’ve grouped them here for your convenience.

Properties of the Powers of Two

Binary numbers are made of powers of two; these articles discuss their properties:

Properties of Binary Numbers

These articles discuss properties of binary numerals:

Binary Arithmetic

These articles discuss binary arithmetic:


These articles discuss bicimals, the binary equivalent of decimals:

Binary Palindromes

These articles discuss binary palindromes (numbers like 1001001):

Visualizing Binary Numbers

These articles discuss ways to visualize binary numbers:

Correctly Rounded Decimal to Floating-Point Conversion

These articles discuss conversion of decimal strings to floating-point binary numbers:

Correctly Rounded Floating-Point to Decimal Conversion

These articles discuss conversion of floating-point binary numbers to decimal strings:

Printing the Contents of a Floating-Point Variable

These articles show different ways to display the exact contents of an IEEE 754 floating-point variable:

The Theory Behind Round-Trip Floating-Point Conversions

These articles discuss the mathematics that govern round-trip floating-point conversions:


4 Responses to “Topics”

  1. Adam Says:

    Thx for interesting informations. Can you add :
    * finding repeating paterns in binary ( for example :
    1/6 = 0.0(01)= 0.00101010101010101010…
    where () show repeating pattern
    * expand converter to use also such notation. For example 0.((001)^{88}010)

    see for more info :


  2. Rick Regan Says:


    These two online converters handle repeating binary; they may be helpful to you:

  3. Joe Says:

    Thanks Rick for this helpful website. I am a teacher of Maths in Zambia, and presently my challenge is how to teach Grade 8s conversions of decimals to bicimals. For example what would be the easiest way to convert 19.525 to bicimal? Step by step please, HELP!

    Thanks once more.

  4. Rick Regan Says:


    The best way is to do it in two steps, first converting the integer part, and then converting the fractional part. For the algorithms, take a look at my article Base Conversion in PHP Using BCMath, in particular the sections labeled “dec2bin_i()” and “dec2bin_f()”.

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