Systematic method of using a calculator to convert “fractional” values to other number systems bases.

Harry Franz
UHD, Houston, Texas

Many calculators only automatically convert integer values from a number system base to another. The typical bases available are decimal, binary, octal, and hexadecimal. Often it is useful to be able to use the calculator to convert “fractional” values from one number base to another.

This method basically shifts the fractional part to an integer value, uses the automatic conversion feature of the calculator, then shifts the converted value back to the proper radix point position.

This method could be programmed into a calculator either by the user or manufacturer. The part to consider the most is to use the biggest power value for the multiplier of the final base , without exceeding the limits of the calculator.

Example convert   0.1234 in decimal to binary

Multiply 0.1234 by the biggest possible power of two, since it is to be converted to binary.

  0.1234₁₀  x   2¹⁰ =126.3616 ₁₀ 

Convert integer part auto. > 1111110₂

Shift Back 10 places > 0.000111111₂     

Example convert  0.163 in decimal to octal

Multiply 0.163 by the biggest power of eight, since it is to be converted to octal.

0.163_{10    x}   8¹⁰  = 175019917.3 ₁₀

Convert integer part auto. >1233513615₈

Shift Back 10 Places > 0.1233513615 ₈     

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