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Thank you so so much.

The reason the method for finding the decimal works is because 0.1011 for example is 2^-1 * 1 + 2^-2 * 0 + 2^-3 * 1 + 2^4 * 1 = 0.6875 When you convert something like 0.6875 back to binary, you are going to consider the digits from left to right. Algebraically, you are finding 2^-1 * a1 + 2^-2 * a2 + 2^-3 * a3 ... = 0.6875. where 0<=ai<2. So you are asking how many 2^-1's can fit in 0.6875 to find a1 (Which is 1 because you can fit 0.5 once in 0.6875), then once you find a1, you subtract 2^-1*a1 on both sides to get 2^-2 * a2 + 2^-3 * a3 ... = 0.6875 - 2^-1 * a1 = 0.1875, and you do this recursively until you find all the digits. The reason the trick with the multiplcation by 2 works is because 2^-1 * a1 + 2^-2 * a2 + 2^-3 * a3 ... = 0.6875 is equivalent to 2^0*a1 + 2^-1 * a2 + 2^-2 * a3 ... = 0.6875 *2 as all we did was multiply the equation by 2. 2^0 = 1, so the question becomes how many 1's can fit in 0.6875 * 2 = 1.375, which is much easier. Then you do this recursively as before. The reason you have a bias for the exponent instead of using 2's complement is so that you can compare the last 31 bits of the floating point representation as an integer and be able to determine which number is (as an absolute value) larger. With 2's complement, since the leading digit is 1, it would cause negative exponenents to evaluate higher than positive ones, leading to more complex comparsions. The reason we use the fraction bits without losing any information is because due to the nature of scientific numbers, the leading digit is promised to be 1. This also means when you convert from IEEE 754 back to decimal, you need to tag the 1 back on. This means by our current standard there is no way of representing 0. So we define 0 00000000 00000000000000000000000 or 1 00000000 00000000000000000000000 as + and - 0. The exponent being 00000000 is a special case where we start treating the last 23 digits as denormalized, you can find more information online. We use a bias closest to 2^8 / 2 = 128 as possible so we can represent positive and negative exponents equally. They decided to chose 127 because it has some nice properties when dealing with overflows with 1/x.

Thank you so so much. I have an exam tomorrow and I finally understand this concept thanks to your video. Really appreciate it.

so, so helpful thank you!!

but 1 divided by two ... ?! how is the remainder 0 ... let alone zero divided by 2 having remainder 1 ?!

we all are stressed engineers ah

very helpful

Excellent video.

u are so awesome. I had this homework due today and could not figure it out.

How do you know when to stop dividing the decimal? (Besides running out of bits?)

2025🚶‍♂️

And my professor needs to watch this video....🙏🏻....

It has been 9 years and this video is still helping generations of students studying Assembly

Thank you very much, its so easy to follow

God bless you

Your name should be "Life Saver"; you just earned me 10 marks on my exam paper. Thanks!

Appreciate it

the decimal is not equal to the original value 263 something

the confusion at 1:07 🤯

it is humbling to learn from youtube but god was this helpful

THX!!!!!!!!!!!!

who is here in 2024 or 2025 ???

i love your voice

2024❤

Now shee is in NASA

wow this 100% explanation 10Qs so much@

Thank you so much, you are so good at explaining! I wish you well in life

Thank you so much for this video <3 it helped me a lot :)

thanks

nice :)

Thanks Indians for saving our lives😂

Your Video just helped me to understand my prof and solve my assignment. So thank you so much! :)

awesome man! you saved my world

yh im lost i keep trying to do C20E0000 into denary but i keep geting -8.875 using this method but the online cacultor is getting -35.5 whic is the right result

Amazing!

hi ! would you please explain it for negative form too? thanks a lot:)

very well explained

Bri I got taught by a 2 yr old XD

حبيت❤

Thank you so much

Understood everything ! But, a doubt.. what if there's 0.125 ? This decimal will eventually become 1, then what can be done in this case? (I suggest you try it first :) )

this 6 minute video summarised a 2 hour lecture for me, you are the GOAT thank you so much 😭😭😭

Arithmetic?

godsend

Just Fucking Great

godsend

THANK YOU

im not allowed to use a calculator on the exam, i think im cooked

Thank you so much

😘