Given the following pair of decimal numbers:
A = 2.6125 x 101 and B = 4.150390625 x 10-1
a) Compute the binary representation of both A and B using the IEEE-754 single precision floating- point format.
b) Compute A+B in binary using the IEEE-754 single precision floating-point format.
A = 2.6125 x 10^1 = 26.125
B = 4.150390625 x 10^-1 = 0.4150390625
a) Compute the binary representation of both A and B using the IEEE-754 single precision floating- point format.
A = 26.125 = 11010.001
=> 1.1010001 x 2^4
biased exponent - 127+4 = 131 = 10000011
Normalised mantisa = 1010001
The IEEE 754 Single precision
0 01010001 10000011000000000000000
B = 0.4150390625 = 0.0110101001
=> 1.10101001 x 2^-2
biased exponent - 127-2 = 125 = 1111101
Normalised mantisa = 10101001
The IEEE 754 Single precision
0 10101001 11111010000000000000000
b) Compute A+B in binary using the IEEE-754 single precision floating-point format.
A+B = 26.5400390625 = 11010.1000101001
=> 1.10101000101001 x 2^4
biased exponent - 127+4 = 131 = 10000011
Normalised mantisa = 1010001
The IEEE 754 Single precision
0 10101000 10000011000000000000000
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