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#### 6.7.1 Radix Modes

Calc normally displays numbers in decimal (base-10 or radix-10) notation. Calc can actually display in any radix from two (binary) to 36. When the radix is above 10, the letters `A` to `Z` are used as digits. When entering such a number, letter keys are interpreted as potential digits rather than terminating numeric entry mode.

The key sequences `d 2`, `d 8`, `d 6`, and `d 0` select binary, octal, hexadecimal, and decimal as the current display radix, respectively. Numbers can always be entered in any radix, though the current radix is used as a default if you press `#` without any initial digits. A number entered without a `#` is always interpreted as decimal.

To set the radix generally, use `d r` (`calc-radix`) and enter an integer from 2 to 36. You can specify the radix as a numeric prefix argument; otherwise you will be prompted for it.

Integers normally are displayed with however many digits are necessary to represent the integer and no more. The `d z` (`calc-leading-zeros`) command causes integers to be padded out with leading zeros according to the current binary word size. (See Binary Functions, for a discussion of word size.) If the absolute value of the word size is ‘`w`’, all integers are displayed with at least enough digits to represent ‘`(2^w)-1`’ in the current radix. (Larger integers will still be displayed in their entirety.)

Calc can display ‘`w`’-bit integers using two’s complement notation, although this is most useful with the binary, octal and hexadecimal display modes. This option is selected by using the `O` option prefix before setting the display radix, and a negative word size might be appropriate (see Binary Functions). In two’s complement notation, the integers in the (nearly) symmetric interval from ‘`-2^(w-1)`’ to ‘`2^(w-1)-1`’ are represented by the integers from ‘`0`’ to ‘`2^w-1`’: the integers from ‘`0`’ to ‘`2^(w-1)-1`’ are represented by themselves and the integers from ‘`-2^(w-1)`’ to ‘`-1`’ are represented by the integers from ‘`2^(w-1)`’ to ‘`2^w-1`’ (the integer ‘`k`’ is represented by ‘`k+2^w`’). Calc will display a two’s complement integer by the radix (either ‘`2`’, ‘`8`’ or ‘`16`’), two `#` symbols, and then its representation (including any leading zeros necessary to include all ‘`w`’ bits). In a two’s complement display mode, numbers that are not displayed in two’s complement notation (i.e., that aren’t integers from ‘`-2^(w-1)`’ to ‘`2^(w-1)-1`’) will be represented using Calc’s usual notation (in the appropriate radix).

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