Doing Decimal/Binary Conversions with Wolfram Alpha

Wolfram Alpha can do many types of calculations, including conversions between numbers in different bases. I’ll demonstrate by showing examples of decimal to binary and binary to decimal conversion.

Decimal to Binary Conversion

These two expressions are equivalent ways of converting decimal 201 to binary 11001001 (click on the links to do the conversions at Wolfram Alpha):

• 201 to binary
• 201 to base 2

Wolfram Alpha returns the same result for each — here is an example screenshot:

Besides doing the conversion to binary, it does related conversions to base 4, base 8, and base 16. It also gives computer representations of the number: 16-bit and 32-bit unsigned integer, and double-precision floating-point (all are given in little-endian format).

Binary to Decimal Conversion

These four expressions are equivalent ways of converting binary 11001001 to decimal 201:

• 11001001 binary to decimal
• 11001001_2 to decimal
• 0b11001001 to decimal
• 0b11001001 to base 10

Wolfram Alpha returns the same result for each — here is an example screenshot:

Converting Fractional Values

Unlike Google Calculator, Wolfram Alpha can convert fractional values, although only from decimal to binary — not the other way around. Here are some examples (screenshots are omitted, and only the main results are shown):

• Convert sum of negative powers of two to binary

  2^-1 + 2^-2 + 2^-4 to binary

  • Result: 0.1101₂
• Convert dyadic fraction to binary

  5,404,319,552,844,595/2^53 to binary

  • Result: 0.10011001100110011001100110011001100110011001100110011₂

    (By the way, this is the double-precision floating-point estimate of 0.6.)

• Convert a decimal fraction to binary

  0.1 to binary

  • Result: 0.00011001100110011₂

    (The result is actually infinite, but is truncated to 17 bits.)