Assume we are using the simple model for floating-point representation as given in this book (the representation uses a 14-bit format, 5 bits for the exponent with a bias of 15, a normalized mantissa of 8 bits, and a single sign bit for the number): a) Show how the computer would represent the numbers 100.0 and 0.25 using this floating-point format.
a) Converting given 100.0 into binary.
10010= 11001002
Converting binary number to the power of 2
1100100.0 = 0.1100100*27
Therefore the value of the exponent is 7.
Convert the exponent into 15 bits excess. So by adding 15 to 7 it becomes 22
15+7=22
Converting 22 to binary = 101102
Sign bit = 0
Exponent(5 bits) = 10110
Significant bits of 8 = 11001000
So the 14-bit floating-point representation of 100.0 is 01011011001000
Now, Converting 0.25 to binary
0.2510 = 0.012
Converting binary number to the power of 2
0.01 = 0.1*2-1
Value of exponent is -1.
Convert the exponent into 15 bits excess. So by adding 15 to -1 it becomes 14
15-1=14
142=011102
Sign bit = 0
Exponent(5 bits) = 01110
Significant bits of 8 = 10000000
So the 14-bit floating-point representation of 0.25 is 00111010000000
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