Reading: IEEE Floating-Point Representation

Stone & Rebelsky: IEEE Floating-Point Representation of Real Numbers

Please submit a question by 9 p.m. on Sunday, 13 February 2011.

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I understood the reading.

It doesn't seem to make much sense to me.

The reading was clear.

I feel as though this is a difficult reading to comprehend. Could you go over it in class?

I think I understand it.

I could not think of a question. If I go back to it and come up with one, I'll let you know.

I don't seem to really have a question for this reading.

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Is it more efficiant to write numbers in octal or hexadecimal, because it's faster for the computer to convert into binary then decimal, or is there no real difference?

We use octal and decimal because it's easier to think of them. Conversion is relatively trivial.

Are there such things as triple precision representation?

Not that I know of.

Is the 'bias' in the exponent bits equivalent to the excess 2^(m-1) notation?

Similar.

If numbers such as 7/5 are cut off in binary representation, how do you express them on the screen and in computations? Are you just required to use a different system?

You cannot represent them exactly with this typical floating-point representation. You must choose a different representation.

This system seems to have the same problem as the signed magnitude's counting system, wherein there are two representations of 0. Does this cause the same problems in IEEE as it does in signed magnitudes?"

It causes some problems.

What are the values of the placeholders for a binary expansion? i.e., in this: "7/5 has an infinite binary expansion 1.011001100110011001100." how would you convert the post-decimal point part into base 10?

1 + 0/2 + 1/4 + 1/8 + 0/16 + 0/32 + 1/64 + 1/128 + ....

How is the decimal to binary and binary to decimal conversion done? It's kind of confusing.

We'l go over it a bit more.

Why does exponent come before mantissa in the binary representation, when in real life people first write mantissa and then the exponent?

It turns out that certain exponents change how we interpret the significand.

When talking about scientific notation, what is the base of numeration?

The base used in times bⁿ.

Can you re-explain biased values and mantissa?

Yes.

Does the bias differ depending on whether you use signed magnitude, One's/Two's complement, or excess 2^(m-1)?

Bias is like excess 2^(m-1).

Is IEEE used in C as well? Because the section just says its used in C..."

Usually.

Is this why there are 32 bit and 64 bit systems?

No.

Are there any drawbacks with 64 bits? (by this I mean in terms of operating other programs.)

It takes more memory.