THE IEEE half (16 bit) precision floating-point format uses 1 bit for the sign, 5 bits for the exponent, and 10 bits for the fraction.

1) estimate the overflow, underflow, and round-off values
2) Find the representation of pi.



Hi could anyone help me get started on this problem? I'm new to numerical computations and would appreciate a supplementary explanation of bits, underflow, overflow, round-off values.

Can pay FG for help if necessary.

carteblanche, saber?

i originally spent a fair bit of time showing some digits of pi step by step. then accidentally refreshed and lost it so i said fuggit. do you know how to convert a decimal number to binary floating point and just having problems with pi? or you dont know how to convert at all?

what don't you understand about bits?

iirc underflow is a value too small to represent and overflow is a value too large to represent. not sure what "estimate overflow value" means, unless it wants the first value too large to represent? round-off, i assume, refers to adding decimal values and getting an unexpected decimal result. like adding 1/3 + 1/3 + 1/3 and not getting 1.0, but not sure what the round-off "value" would be. it's been close to a decade since i studied IEEE format, and i dont really feel like googling the terms.

This post was edited by carteblanche on Sep 11 2015 10:43pm

i don't understand how bits relates to 1) and 2)

clearly we have to use the information given about the format of the precision floating-point of IEEE to answer 1) and 2) but that's all I know

This post was edited by Tamagochi on Sep 12 2015 11:20am

do you know what the IEEE 16 bit floating format is? i'm not clear how you could accomplish either 1 or 2 without taking bits into account.



gonna copy a few examples from wiki:



so for #2 you just represent pi best you can using these 16 bits

underflow/overflow depends completely on the bits. the bits allow you to represent quite a range of numbers, but the problem is not every number in the range can be represented.

This post was edited by carteblanche on Sep 12 2015 12:05pm

0 01111 0000000000 = 1

could you explain this to me?

short answer: 2^ (15 - 15) = 2^0 = 1

longer answer, look at the chart:

sign is 0, so it's positive.
look at the exponent now. exponent is 01111 = 15
look at the fractional component: 0000000000 = 0


so building the number:
2^(exponent - (2^(exponent bits - 1) - 1)) + fractional component
2^(exponent - (2^(5-1)-1)) + fractional component
2^(exponent - (2^4-1)) + fractional component
2^(exponent - 15) + fractional component
2^(15 - 15) + 0
= 2^0 + 0
= 1 + 0
= 1

it's easier to find tutorials for 32 bit floating points. 16 bit work the same way, just fewer bits



This post was edited by carteblanche on Sep 12 2015 02:59pm

Ok thanks that helped me understand this a bit better.

I'm having trouble with this problem:

Write a Matlab function whose input is a positive number in base 10 and output is a string showing the number in base 12.
I think I get the idea of what needs to be done but I've only been using Matlab for a brief while so I would appreciate any help in starting the code.

i assume "positive number" means a 32 bit integer?

start with pseudo code to get your logic down, then convert the syntax to matlab.

not sure