This section describes the rules that the text interpreter uses when it tries to convert a string into a number.

Let <digit> represent any character that is a legal digit in the current
number base^{1}.

Let <decimal digit> represent any character in the range 0-9.

Let {*a b*} represent the *optional* presence of any of the characters
in the braces (*a* or *b* or neither).

Let * represent any number of instances of the previous character (including none).

Let any other character represent itself.

Now, the conversion rules are:

- A string of the form <digit><digit>* is treated as a single-precision (cell-sized) positive integer. Examples are 0 123 6784532 32343212343456 42
- A string of the form -<digit><digit>* is treated as a single-precision (cell-sized) negative integer, and is represented using 2's-complement arithmetic. Examples are -45 -5681 -0
- A string of the form <digit><digit>*.<digit>* is treated as a double-precision (double-cell-sized) positive integer. Examples are 3465. 3.465 34.65 (all three of these represent the same number).
- A string of the form -<digit><digit>*.<digit>* is treated as a double-precision (double-cell-sized) negative integer, and is represented using 2's-complement arithmetic. Examples are -3465. -3.465 -34.65 (all three of these represent the same number).
- A string of the form {+ -}<decimal digit>{.}<decimal digit>*{e E}{+ -}<decimal digit><decimal digit>* is treated as a floating-point number. Examples are 1e 1e0 1.e 1.e0 +1e+0 (which all represent the same number) +12.E-4

By default, the number base used for integer number conversion is
given by the contents of the variable `base`

. Note that a lot of
confusion can result from unexpected values of `base`

. If you
change `base`

anywhere, make sure to save the old value and
restore it afterwards; better yet, use `base-execute`

, which does
this for you. In general I recommend keeping `base`

decimal, and
using the prefixes described below for the popular non-decimal bases.

`dpl`

– a-addrgforth “dpl”

`User`

variable – *a-addr* is the address of a cell that stores the
position of the decimal point in the most recent numeric conversion.
Initialised to -1. After the conversion of a number containing no
decimal point, `dpl`

is -1. After the conversion of `2.`

it holds
0. After the conversion of 234123.9 it contains 1, and so forth.

`base-execute`

i*x xt u – j*xgforth “base-execute”

execute *xt* with the content of `BASE`

being *u*, and
restoring the original `BASE`

afterwards.

`base`

– a-addrcore “base”

`User`

variable – *a-addr* is the address of a cell that
stores the number base used by default for number conversion during
input and output. Don't store to `base`

, use
`base-execute`

instead.

`hex`

–core-ext “hex”

Set `base`

to &16 (hexadecimal). Don't use `hex`

,
use `base-execute`

instead.

`decimal`

–core “decimal”

Set `base`

to &10 (decimal). Don't use `decimal`

, use
`base-execute`

instead.

Gforth allows you to override the value of `base`

by using a
prefix^{2} before the first digit
of an (integer) number. The following prefixes are supported:

`&`

– decimal`#`

– decimal`%`

– binary`$`

– hexadecimal`0x`

– hexadecimal, if base<33.`'`

– numeric value (e.g., ASCII code) of next character; an optional`'`

may be present after the character.

Here are some examples, with the equivalent decimal number shown after in braces:

-$41 (-65), %1001101 (205), %1001.0001 (145 - a double-precision number), 'A (65), -'a' (-97), &905 (905), $abc (2478), $ABC (2478).

Number conversion has a number of traps for the unwary:

- You cannot determine the current number base using the code sequence
`base @ .`

– the number base is always 10 in the current number base. Instead, use something like`base @ dec.`

- If the number base is set to a value greater than 14 (for example, hexadecimal), the number 123E4 is ambiguous; the conversion rules allow it to be intepreted as either a single-precision integer or a floating-point number (Gforth treats it as an integer). The ambiguity can be resolved by explicitly stating the sign of the mantissa and/or exponent: 123E+4 or +123E4 – if the number base is decimal, no ambiguity arises; either representation will be treated as a floating-point number.
- There is a word
`bin`

but it does*not*set the number base! It is used to specify file types. - ANS Forth requires the
`.`

of a double-precision number to be the final character in the string. Gforth allows the`.`

to be anywhere after the first digit. - The number conversion process does not check for overflow.
- In an ANS Forth program
`base`

is required to be decimal when converting floating-point numbers. In Gforth, number conversion to floating-point numbers always uses base &10, irrespective of the value of`base`

.

You can read numbers into your programs with the words described in Line input and conversion.

[1] For example, 0-9 when the number base is decimal or 0-9, A-F when the number base is hexadecimal.

[2] Some Forth implementations provide a similar scheme by
implementing `$`

etc. as parsing words that process the subsequent
number in the input stream and push it onto the stack. For example, see
Number Conversion and Literals, by Wil Baden; Forth Dimensions
20(3) pages 26–27. In such implementations, unlike in Gforth, a space
is required between the prefix and the number.