Texas Instruments TI89 Developer Guide - Page 205
Numbers, integer 65534 is 254 255 2 NONNEGATIVE_INTEGER_TAG. - fraction to decimal
UPC - 033317198566
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Chapter 15: Expressions and The Expression Stack 163 15.2.2. constants true and false, and most built-in mathematics functions and operators are represented using a single tag. Floating-point numbers, rational numbers, and integer numbers each require an identifier tag on top of the standard representation of the number. All of the tag values are defined in tiams.h. Each of the tag names ends with the characters "_TAG." The following sections describe the various tags and what they identify or represent. Numbers The Operating System includes two separate number systems - the rational number system which contains tagged integers and tagged fractions, and the floating-point number system, which uses Binary Coded Decimal (BCD) floating-point numbers. A primary difference between these number systems is that the rational system is by definition exact and the floating-point system is assumed always to be an approximation. In the rational system the number of digits is limited but not fixed. If an arithmetic operation on two rational numbers completes successfully, then the result is exact. No loss of precision occurs. In the floating-point system the number of digits is fixed, and therefore, loss of precision is always a possibility. Thus, the result of a floating-point operation is considered to be an approximation. The rational numbers include tagged integers and tagged fractions. The term tagged integer is used to distinguish these numbers from the C programming types - int, short, long, etc. A tagged integer has three elements - a tag at the highest address, a length, and a magnitude. An integer magnitude is represented as a sequence of adjacent quantums, with the least significant quantum deepest (lowest address) and the most significant quantum nonzero. For example, the 16 bit integer 65534 (0xFFFE) would appear as 254 255 (0xFE 0xFF) with the least significant quantum deepest. A sized integer magnitude is a one-quantum length field on top of an integer magnitude. With the quantum size of one byte, the length can be 0 through 255 quantums, and the maximum possible sized integer magnitude is 256255 - 1 ≈ 10614. Thus, the sized integer magnitude for the integer 65534 would appear as 254 255 2 (0xFE 0xFF 0x2). A non-negative integer is represented as a NONNEGATIVE_INTEGER_TAG on top of a sized integer magnitude. Thus, the tagged integer representation of the integer 65534 is 254 255 2 NONNEGATIVE_INTEGER_TAG. A negative integer is represented as a NEGATIVE_INTEGER_TAG on top of a sized integer magnitude. So, the tagged integer representation of the negative integer L65534 is 254 255 2 NEGATIVE_INTEGER_TAG. TI-89 / TI-92 Plus Developer Guide Not for Distribution Beta Version January 26, 2001