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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
1
●
1
1
1
0
0
1
0
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 = 111110 (shift left until first two characters are 10
Exponent = 1010 (Subtract offset from exponent value 10
Offset = 3 (Adjustment required to Mantissa and Exponent)
Answer
Mantissa = 110000
Exponent = 0111
Offset = 3
Mantissa
Exponent
1
●
1
0
0
0
0
0
1
1
1
Mantissa
Exponent
1
●
1
1
1
1
0
1
0
1
0
Normalised
Not Normalised
What is the Normalised Floating Point representation of the denary value
-0.1875
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 = -0.0011
Answer
Denary = -0.1875
Fixed Point Binary Value = -0.0011
Mantissa = -011000
Mantissa = 101000
Exponent Value = -2
Exponent = 1110
Mantissa
Exponent
1
●
0
1
0
0
0
1
1
1
0
The following is the binary floating point representation of a number
Mantissa
Exponent
1
●
0
1
1
1
1
1
0
0
0
Calculate the denary equivalent of the number
Clue
Standard Form = -0.10001 x 2
-8
Mantissa
Exponent
-1
1⁄2
1⁄4
1⁄8
1⁄16
1⁄32
-8
4
2
1
1
●
0
1
1
1
1
1
0
0
0
Answer
Exponent = 1000
Exponent Value = -8
Mantissa = 101111 (Two's Complement)
Mantissa = -010001 (Signed Value)
Standard Form = -0.10001 x 2
-8
Fixed Point Binary Value = -0.0000000010001
Denary Value =
-0.0020751953125
Mantissa
Exponent
-1
1⁄2
1⁄4
1⁄8
1⁄16
1⁄32
-8
4
2
1
1
●
0
1
1
1
1
1
0
0
0
The following is an approximate binary floating point representation of the number 0.63
Mantissa
Exponent
0
●
1
0
1
0
0
0
0
0
0
Calculate the denary equivalent of the binary number
Clue
Standard Form = 0.10100 x 2
0
Mantissa
Exponent
-1
1⁄2
1⁄4
1⁄8
1⁄16
1⁄32
-8
4
2
1
0
●
1
0
1
0
0
0
0
0
0
Answer: Denary Equivalent
Exponent = 0000
Exponent Value = 0
Mantissa = 010100 (Two's Complement)
Standard Form = 0.10100 x 2
0
Fixed Point Binary Value = 0.101
Denary =
0.625
Mantissa
Exponent
-1
1⁄2
1⁄4
1⁄8
1⁄16
1⁄32
-8
4
2
1
0
●
1
0
1
0
0
0
0
0
0
