Consider the following IEEE floating point numbers A & B A 0 1000101 01101101011
ID: 3883913 • Letter: C
Question
Consider the following IEEE floating point numbers A & B
A
0
1000101
01101101011000000000000
B
0
0111110
00101000000000000000000
a) Find out the no’s A & B is decimal.
b) Perform A ÷ B Show the calculation step by step
(Normalize and truncate the result if required)
A
0
1000101
01101101011000000000000
B
0
0111110
00101000000000000000000
8. Consider the following IEEE floating point numbers A & B A 0 1000101 01101101011000000000000 00101000000000000000000 a) Find out the no's A & B is decimal. b) Perform A ÷ B Show the calculation step by step (Normalize and truncate the result if required)Explanation / Answer
The IEEE floating point representation is a form to represent numbers in scientific format using a base and exponent.
The representation consist of 3 parts:
1. Sign Bit - 1 digit which denotes the sign of number to be represented. 0 means positive while 1 means negative.
2. Exponent - Second part is usually a 7-bit number that represents the power of 2 in the scientific representation of that number.
3. Mantissa - The matissa part of IEEE numbers (consisting of 23 bits) represent the precision bits (decimal digits) of number.
So the IEEE floating point format represents a deciam lin given way: ((1)^sign bit)(1+fraction)×2^(exponent - 127)
A -
Sign bit = 0 ==> positive
Exponent = 1000101 base 2 = 69 in decimal system
Mantissa = 0.01101101011000000000000 = 0.42724609375
Thus, A = +0.42724609375 * (2^(69-127)) = +0.42724609375 *2^(-58)
B -
Sign bit = 0 ==> positive
Exponent = 0111110 base 2 = 62 in decimal system
Mantissa = 0.00101000000000000000000 = 0.15625
Thus, B = +0.15625 * (2^(62-127)) = +0.15625 *2^(-65)
Therefore, A/B = 2.73 * (2^7) = 350
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