Apple II User Manual
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)
0 10000000 ($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