Base-N Calculations
In DreamCalc, base-N calculations are performed in one of three modes, as follows.
- 32 Bit 2s Complement Integer
Integer values only of 4 bytes or less.
- 64 Bit 2s Complement Integer
Integer values only of 8 bytes or less.
- Floating Point Base-N Mode
Floating point values with 8 byte mantissa & independent sign.
These are distinct from the "Normal Math" mode, even if you set the radix to be decimal. When base-N is
enabled, you have the option of selecting the radix and performing LOGIC calculations. You also have the ability
to perform mathematical calculations, but you should be aware of base-N range restrictions and integer
rounding.
To change the base-N mode, use the Modes→Base-N Modes main menu. Alternatively, use the
calculator's [MODE] key.
Setting the Radix
In all base-N modes, you may set the radix to any value between 2 and 16. You'll find you can set commonly
used bases, such as decimal, hexadecimal, octal and binary, from the keypad at the touch of a button. Changing
the radix does not reset the display — the display value is simply converted. For bases higher than 10, use the
keys marked A - F as digits. Additional radix settings can be found under the
Modes→Base-N→Other Radix menu, or may be set using the [MODE] key.
Digit Grouping & Padding
You may set digit grouping every four characters for bases which align to byte boundaries, as follows:
- Binary - nibble grouping
- Quadrary - byte grouping
- Hexadecimal - word grouping
For all other bases, digits are not grouped, except decimal which will group in thousands as in Normal Math
mode. Digit grouping is enabled by default.
You can also enable or disable zero padding of lead digits. When enabled, lead zeros will be displayed so as
to indicate the position of every available digit. Leading zeros are not shown in the decimal radix. This
setting is disabled by default.
Both these settings are available from the Numeric Screen page of the Options
Window or by using [MODE] key in base-n mode.
Base-N Arithmetic
Integer 2s Complement
In integer 2s complement arithmetic, negative numbers are represented as the value that, when added to a
positive number of the same magnitude, equals zero. A negative value is formed by complementing each binary bit
of the positive number, and then adding 1. For negative values, the most significant bit (MSB) is always 1. This
arithmetic is commonly used by computers when dealing with integers.
In decimal, the minus sign character is used to indicate negative values, but in all other bases it is not
shown.
Here is an example in the 32 bit integer mode for hexadecimal radix:
1
[-]
2
[ENTER]
Displays: FFFF FFFF
Converting this value to decimal will show -1.
Hint: In the Numeric Screen page of the Options Window, you will find
an option to show negative values in red. This setting will highlight negative 2s complement values.
Floating Point
In floating point base-N mode, 2s complement arithmetic is not used and the sign is held independently. Thus,
there are 64 bits of precision plus one extra sign flag. In this mode, the decimal value -1 will be shown as
-0x1 when converted to hexadecimal.
The permissible numerical range in floating point base-n mode is +/-18446744073709551615. In the decimal
radix, therefore, a maximum of 20 digits is allowed where necessary, but often DreamCalc will present results
using only 18 decimal digits. This behavior is normal and ensures accuracy of +/-1 of the last digit. Similarly,
rounding is done in other radix as applicable.
See also: Integer & Logic Functions
