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Floating Point Binary
Floating Point Binary
Current size definition
Normalised floating point binary representation with a mantissa and exponent both in two's complement binary
Mantissa:
6
Exponent:
4
Valid range for positive values:
0.001953125 to 124
0.000000001 to 1111100
Valid range for negative values:
-0.001953125 to -128
-0.000000001 to -10000000
Change the size of the mantissa and exponent
Select the size of the mantissa
3
4
5
6
7
8
10
12
Select the size of the exponent
3
4
5
6
The following is the floating point representation of a number
Mantissa
Exponent
0
●
0
1
0
0
1
0
1
0
1
The value is not normalised. What is the normalised form of this binary number?
Mantissa
0
1
0
1
0
1
0
1
0
1
0
1
Exponent
0
1
0
1
0
1
0
1
Clue
Mantissa = 001001 (shift left until first two characters are 10
Exponent = 0101 (Subtract offset from exponent value 5
Offset = 1 (Adjustment required to Mantissa and Exponent)
Answer
Mantissa = 010010
Exponent = 0100
Offset = 1
Mantissa
Exponent
0
●
1
0
0
1
0
0
1
0
0
Mantissa
Exponent
0
●
0
1
0
0
1
0
1
0
1
Normalised
Not Normalised
What is the Normalised Floating Point representation of the denary value
-2.75
Mantissa
0
1
0
1
0
1
0
1
0
1
0
1
Exponent
0
1
0
1
0
1
0
1
Clue
Fixed Point Binary Value = -10.11
Answer
Denary = -2.75
Fixed Point Binary Value = -10.11
Mantissa = -010110
Mantissa = 101010
Exponent Value = 2
Exponent = 0010
Mantissa
Exponent
1
●
0
1
0
1
0
0
0
1
0
The following is the binary floating point representation of a number
Mantissa
Exponent
1
●
0
1
0
0
0
1
1
1
0
Calculate the denary equivalent of the number
Clue
Standard Form = -0.11000 x 2
-2
Mantissa
Exponent
-1
1⁄2
1⁄4
1⁄8
1⁄16
1⁄32
-8
4
2
1
1
●
0
1
0
0
0
1
1
1
0
Answer
Exponent = 1110
Exponent Value = -2
Mantissa = 101000 (Two's Complement)
Mantissa = -011000 (Signed Value)
Standard Form = -0.11000 x 2
-2
Fixed Point Binary Value = -0.0011
Denary Value =
-0.1875
Mantissa
Exponent
-1
1⁄2
1⁄4
1⁄8
1⁄16
1⁄32
-8
4
2
1
1
●
0
1
0
0
0
1
1
1
0
The following is an approximate binary floating point representation of the number 0.69
Mantissa
Exponent
0
●
1
0
1
1
0
0
0
0
0
Calculate the denary equivalent of the binary number
Clue
Standard Form = 0.10110 x 2
0
Mantissa
Exponent
-1
1⁄2
1⁄4
1⁄8
1⁄16
1⁄32
-8
4
2
1
0
●
1
0
1
1
0
0
0
0
0
Answer: Denary Equivalent
Exponent = 0000
Exponent Value = 0
Mantissa = 010110 (Two's Complement)
Standard Form = 0.10110 x 2
0
Fixed Point Binary Value = 0.1011
Denary =
0.6875
Mantissa
Exponent
-1
1⁄2
1⁄4
1⁄8
1⁄16
1⁄32
-8
4
2
1
0
●
1
0
1
1
0
0
0
0
0
