Number formats¶

There are multiple number formats among the protocols and formats around CASIO calculators. The following sections describe some of them.

CASIOLINK-style BCD¶

Numbers with the CASIOLINK family of protocols and file formats are represented using 10 bytes, i.e. 20 nibbles (groups of 4 bits).

Assuming we use 0-based indexing:

Nibbles 0 to 15 (i.e. bytes 0 to 7) represent the mantissa, with one nibble per digit.
Nibbles 16 and 17 (i.e. byte 8) contains the flags.
Nibbles 18 and 19 (i.e. byte 9) is the exponent of the number, with one nibble per digit.

Todo

What I wrote at the time about these numbers is these values for the flags, not sure how they combine:

0x80 is “special”, possibly meaning infinite values and such?
0x50 is “negative”, it said “the negative is two bits/flags (I don’t know why)”, so that may be great to determine.
0x01 is “pow neg”, meaning that the power is negative.

Todo

Provide an example here.

fx-9860G-style BCD¶

Numbers with the fx-9860G and compatible are represented using 12 bytes, i.e. 24 nibbles, with only the first 9 bytes, i.e. 18 nibbles, being significant.

Assuming we use 0-based indexing:

Nibbles 0 to 2 represent the exponent and sign, with the following ranges:

Raw range

Sign

Real range

000 - 499

+

-99 - 399

500 - 999

-

-99 - 399
Nibbles 3 to 17 represent the mantissa, starting from 10^0.

Raw range	Sign	Real range
000 - 499	`+`	-99 - 399
500 - 999	`-`	-99 - 399

Examples are the following:

Raw number (1 digit / nib.)	Sign	Exponent	Mantissa	Result
`600 123000000000000 xxxxxx`	`-`	`1` (`600 - 100 - 99`)	`.123`	`-1.23`
`100 230400000000000 xxxxxx`	`+`	`1` (`100 - 99`)	`.2304`	`2.304`
`098 456000000000000 xxxxxx`	`-`	`-1` (`98 - 99`)	`.456`	`.0456`
`597 786000000000000 xxxxxx`	`-`	`-2` (`597 - 500 - 99`)	`.786`	`-.00786`

fx-9860G-style fraction¶

Fractions with the fx-9860G and compatible are represented using 12 bytes, i.e. 24 nibbles, with only the first 9 bytes, i.e. 18 nibbles, being significant.

Assuming we use 0-based indexing:

Nibble 0 represents the sign (1 for positive, 6 for negative);
Nibble 1 is always A;
Nibble 2 is the number of nibbles to read after, minus 1.

Examples are the following:

Raw number (1 digit)	Sign	`a`	`b`	`c`	Result
`6A 6 2 A 33 A 50 00000000 xxxxxx`	`-`	`2`	`33`	`50`	`-2 * (33 / 50)`
`1A 7 2 A 33 A 500 0000000 xxxxxx`	`+`	`2`	`33`	`500`	`2 * (33 / 500)`