Apple II manual Stored, High LOW EXP Mantissa, Floating Point Representation Examples

The exponent is a binary scaling factor (power of two) which is applied to the mantissa. Ranging from -128 to +127, the exponent is stored in standard two's complement representation except for the sign bit which is complemented. This representation allows direct comparison of exponents, since they are stored in increasing numerical sequence. The most negative exponent, corresponding to the smallest magnItude, -128, is stored as $00 ($ means hexidecimal) and the most positive, +127, is stored as $FF (all ones).

EXPONENT	STORED	AS
+127	11111111	($FF)
+3	10000011	($83)
+2	10000010	($82)
+1	10000001	($81)

010000000 ($80)

-1 01111111 ($7F)

-2 01111110 ($7E)

-3 01111101 ($7D)

-128 00000000 ($00)

The smallest magnitude which can be represented is 2^-150.

	_____		_____		_____		_____
0		0		0		1
_____		_____		_____		_____
			HIGH				LOW
	EXP			MANTISSA

The largest positive magnitude which can be represented is +2^128-1.

_____		_____	_____			_____
$7F $7F $FF $FF
_____	_____ _____				_____
EXP			MANTISSA
FLOATING POINT		REPRESENTATION EXAMPLES
DECIMAL		HEX		HEX
NUMBER	EXPONENT		MANTISSA
+ 3		81	60	00	00
+ 4		82	40	00	00
+ 5		82	50	00	00
+ 7		82	70	00	00
+12		83	60	00	00
+15		83	78	00	00
+17		84	44	00	00
+20		84	50	00	00
+60		85	78	00	00