I need help with my numerical analysis homework... here's the question?

[Keith]

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 machine-size number. Find the latter.

Problem: An UNDERFLOW is any positive number smaller than the smallest positive machine-size number. Find the latter.

If you have an answer please explain the work as well, it would be greatly appreciated! Thanks in advance!

[ryuku32]

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.