Intel 80286, 80287 manual Binary Integers

	OVERVIEW OF NUMERIC PROCESSING
	Table 1-5. Real Number Notation
Notation			Value
Ordinary Decimal	178.125
Scientific Decimal	1A78125E2
Scientific Binary	1A0110010001E111
Scientific Binary	1A0110010001E10000110
(Biased Exponent)
80287 Short Real	Sign	Biased Exponent	Significand
(Normalized)	0	10000110	~100100010000000000000

1A (implicit)

BINARY INTEGERS

The three binary integer formats are identical except for length, which governs the range that can be accommodated in each format. The leftmost bit is interpreted as the number's sign: O=positive and 1= negative. Negative numbers are represented in standard two's complement notation (the binary integers are the only 80287 format to use two's complement). The quantity zero is represented with a positive sign (all bits are 0). The 80287 word integer format is identical to the 16-bit signed integer data type of the 80286.

DECIMAL INTEGERS

Decimal integers are stored in packed decimal notation, with two decimal digits "packed" into each byte, except the leftmost byte, which carries the sign bit (O=positive, 1= negative). Negative numbers are not stored in two's complement form and are distinguished from positive numbers only by the sign bit. The most significant digit of the number is the leftmost digit. All digits must be in the range OH-9H.

REAL NUMBERS

The 80287 stores real numbers in a three-field binary format that resembles scientific, or exponential, notation. The number's significant digits are held in the significand field, the exponent field locates the binary point within the significant digits (and therefore determines the number's magnitude), and the sign field indicates whether the number is positive or negative. (The exponent and significand are analogous to the terms "characteristic" and "mantissa" used to describe floating point numbers on some computers.) Negative numbers differ from positive numbers only in the sign bits of their significands.

Table 1-5 shows how the real number 178.125 (decimal) is stored in the 80287 short real format. The table lists a progression of equivalent notations that express the same value to show how a number can be converted from one form to another. The ASM286 and PL/M-286 language translators perform a similar process when they encounter programmer-defined real number constants. Note that not every decimal fraction has an exact binary equivalent. The decimal number 1/10, for example, cannot be expressed exactly in binary Gust as the number 1/3 cannot be expressed exactly in decimal). When a translator encounters such a value, it produces a rounded binary approximation of the decimal value.

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