#### 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 Number 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 Number 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).