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(b) Calculation example
Calculation examples are shown below. (The "X" in (nnnnnn) x indicates the numeral system used.)
1) Storing "10"
(10)
10
(1010)
2
(1.010000..... 2
3
)
2
Sign: Positive 0
Exponent: 3 401H (100 0000 0001)
2
Mantissa: (0100 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000)
2
In this case, the value will be encoded as 4014000000000000H.
2) Storing "0.75"
(0.75)
10
(0.11)
2
(1.100..... 2
-1
)
2
Sign: Positive 0
Exponent: -1 3FDH (011 1111 1101)2
Mantissa: (1000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000)2
In this case, the value will be encoded as 3FD8000000000000H.
Values after the decimal point (in binary) is calculated as follows.
(0.1101)
2
(0.1101)
2 = 2
-1
+ 2
-2
+ 2
-4
= 0.5 + 0.25 + 0.0625 = (0.8125)10
0.1101
The bit represents 2
-1
The bit represents 2
-2
The bit represents 2
-3
The bit represents 2
-4
Sign Exponent Mantissa
0 100000000010100000000000000000000000000000000000000000000000000
4 014000000000000
Sign Exponent Mantissa
0 011111111011000000000000000000000000000000000000000000000000000
3 FD8000000000000
Example