
I need help with my numerical analysis homework... here's the question?
We are given a "fictitious" machine... The first bit is the sign of the mantissa, the second bit is the sign of the exponent, the next three are the exponent (w/o its sign), and the last eight are the mantissa (w/o its sign). It is required that the leading digit of the mantissa is 1. We use the normalized binary from, i.e., (+/.1*a2*a3*a4*a5*a6*a7*a8) x (2^(+/b1*b2*b3)), where a's and b's are either 0 or 1.
Problem: An OVERFLOW is any number larger than the largest possible machinesize number. Find the latter.
Problem: An UNDERFLOW is any positive number smaller than the smallest positive machinesize number. Find the latter.
If you have an answer please explain the work as well, it would be greatly appreciated! Thanks in advance!

Computational Science was a long time ago, and I don't remember learning much like you, but here goes.
Your largest mantissa is 256, largest exponent is 2^7.
So isn't 256 * 2^7 = 32768, the largest?
I'd think smallest is just 2^7.
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