Texas Instruments TI89 Developer Guide - Page 206

164 Chapter 15: Expressions and The Expression Stack Integer value L5 256 65538 L1000000 Tagged integer representation 5 1 NEGATIVE_INTEGER_TAG 0 1 2 NONNEGATIVE_INTEGER_TAG 2 0 1 3 NONNEGATIVE_INTEGER_TAG 64 66 15 3 NEGATIVE_INTEGER_TAG Table 15.2: Tagged Integer Examples The integer zero is a special case in this representation. Zero has no integer magnitude but is represented simply by a NONNEGATIVE_INTEGER_TAG on top of a zero length field as follows, 0 NONNEGATIVE_INTEGER_TAG. Note that this is the only valid representation of a simple tagged integer zero. The system never generates nor expects a NEGATIVE_INTEGER_TAG on top of a 0 length field nor any tagged integer with a nonzero length field and a zero magnitude. These invalid representations will cause unexpected system behavior. Fractions include two sized integer magnitudes - one for the numerator and one for the denominator. A positive fraction is identified by a POSITIVE_FRACTION_TAG. A negative fraction is identified by a NEGATIVE_FRACTION_TAG. The denominator is placed deepest in the representation, then the numerator, then the tag on top. Fractions are always fully reduced, that is, the greatest common divisor of the numerator and denominator is 1. Fraction value 1/2 L2/3 5/256 L999999/1000000 Tagged fraction representation 2 1 1 1 POSTIVE_FRACTION_TAG 3 1 2 1 NEGATIVE_FRACTION_TAG 0 1 2 5 1 POSITIVE_FRACTION_TAG 64 66 15 3 63 66 15 3 NEGATIVE_FRACTION_TAG Table 15.3: Tagged Fraction Examples The fraction representation includes two special cases. They are called signed zeros. Signed zeros occur when the system performs symbolic operations such as computing limits or simplifying expressions involving infinity. They are represented by a fraction whose numerator is 0 and whose denominator is 1. Thus, +0 is 1 1 0 POSITIVE_FRACTION_TAG, and L0 is 1 1 0 NEGATIVE_FRACTION_TAG. These are the only valid fractions with a zero numerator, and the denominator must be 1. The system does not generate nor expect any other fraction whose numerator or denominator is zero. Invalid fractions will cause unexpected behavior. TI-89 / TI-92 Plus Developer Guide Not for Distribution Beta Version January 26, 2001