On the AQA and Cambridge syllabuses, the text books state that normalized numbers must begin with either 10 (negative) or 01 (positive) in order to guarantee the maximum accuracy of the mantissa and is called normalised float form. This is not the case in IEEE but neither exam boards use IEEE.
The twos compliment version of the exponent is read like this: -127 64 32 16 8 4 2 1 in terms of powers eg the MSB is a negative power. There is no possible arrangement of bit s that can be lower than -127 so 100000000 is the smallest exponent as it represents -127 or 2 to the power -127. If you place a one bit anywhere else it increases the number in twos compliment.
Now the mantissa: your mantissa is not in normal form as it begins with 00 thus breaking the rule of beginning with 01 or 10.The first positive mantissa that follows this rule is 0.100000000.Which is approximately 1 * 2 to power -127.
manpreet![Tuteehub forum best answer]()
Best Answer
2 years ago
In the AQA A2 Computing textbook (Bond and Langfield, 2009), they say that this number is the smallest positive normalised value, given a 10 bit mantissa and a 6 bit exponent:
I don't understand why this is the case. I would have thought that having a mantissa of 0.000000001 would result in the smallest positive value. Could someone explain this to me?