Built-in Mathematica Symbol

BaseForm

BaseForm[expr, n]
prints with the numbers in expr given in base n.

MORE INFORMATION

The maximum allowed base is 36. For bases larger than 10, additional digits are chosen from the letters a-z. »

You can enter a number in an arbitrary base using base^^digits. »

When a number in an arbitrary base is given in scientific notation, the exponent is still given in base 10. »

You can mix BaseForm with NumberForm and related functions. »

BaseForm acts as a "wrapper", which affects printing, but not evaluation.

EXAMPLES

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Basic Examples (2)

A binary integer:

A binary real:

Represent single-digit hexadecimal numbers:

A binary integer:

In[1]:=

Out[1]//BaseForm=

A binary real:

In[2]:=

Out[2]//BaseForm=

Represent single-digit hexadecimal numbers:

In[1]:=

Out[1]//BaseForm=

Scope (5)

Represent a random number in bases 2 through 36:

A complex number formatted in base 3:

An arbitrary-precision number in base 5:

A vector of reals in base 8:

A matrix:

A mixed symbolic and numeric expression with numbers represented in base 12:

Properties & Relations (5)

Exponents are given in base 10:

Input a number in base 16:

Output in base 16:

BaseForm formats numbers in a given base:

IntegerDigits gives a list of the digits:

Convert back to base 10:

IntegerString gives the digits as a string:

Convert the string back to a base-10 number:

Format a real number in base 2:

RealDigits gives a list of the digits and number of digits to the left of the decimal:

Reconstruct the base-10 number from RealDigits output:

Convert a number to base 2:

Represent the number to be precise to 3 decimal digits using NumberForm:

The base must be an integer between 2 and 36:

Neat Examples (1)

Expansions in different bases can be terminating or non-terminating for the same number: