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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 82H (10000010)
2
Mantissa: (010 00000 00000 00000 00000)
2
In this case, the value will be encoded as 41200000H.
2) Storing "0.75"
(0.75)
10
(0.11)
2
(1.100..... 2
-1
)
2
Sign: Positive 0
Exponent: -1 7E
H (01111110)2
Mantissa: (100 00000 00000 00000 00000)2
In this case, the value will be encoded as 3F400000H.
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 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
41 2 00000
0 0 1 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3F4 00000
Sign Exponent Mantissa
Example