Binary 7 – Floating Point Binary Addition

This is the seventh in a series of videos about the binary number system which is fundamental to the operation of a digital electronic computer. In particular, this video covers adding together floating point binary numbers for a given sized mantissa and exponent, both in two’s complement. The addition of numbers in base 10 standard scientific form is examined first, before the same methods are applied to floating point binary numbers. Representation errors resulting from truncation are mentioned, as well as overflow and underflow. The video includes worked examples.

[AlexJoneses]

Makes me happy that videos this high quality are out for free

[redaloui]

Sad to see my specialty channels underrated, my respect and love bro ❤❤👍👍🚀🚀🚀🙏🙏🙏🇩🇿🇩🇿🇩🇿 from lageria

[JVenom_]

never thought addition could be difficult lmao ty for video

[iaderesel]

Awesome videos! Straight to the point, clear explanation, perfect use of the combination of slides and speech

[rollio]

Thank you for this video! I was stuck on this in cosc class but you saved me! You just earned a sub ;)

[yasserothman]

@2:37 the exponent should come first in the binary representation not the mantissa so the exponent is 0100 for the first number right ?

[natesr]

great video
so many shortcuts, push video many times

[leesweets]

This is how we do it on paper, sure, but Is this really how a computer does it algorithmically, or in hardware? Do computers do floating point arithmetic in hardware or would this be an assembly script?

[adumont]

Great video. I'm trying to learn about FP to implement some software FP arithmetics in my 6502 FORTH.

I have a question, when normalized, if the left most bit is always 0, can we not omit it and get one more significant bit in the mantisa? I mean with 6 bit in mantisa we can represent just storing the 6 xs bits instead of a 0 and 5 additional bits. Just a thought

[cohenbore]

do u treat different sub total found on an invoice when normalising in 1NF

[eLBehmo]

Great video! Please explain addition and multiplication for IEEE 754-2008 (base 10) decimal floating point, too!

[thearkhamknight]

@9:20 Is it not -4.5 as opposed to -3.5

[thatboiiii]

How do you do the double check result in this video, I find it difficult for me :<

[sanaomar]

how 1111 which is equal to 15 became -1? please anyone knows?

[dilsedhoni]

@3:12 the result should be 1.1001 X 2^2 after normalization.

[mirhosseinimehrpooya]

list all the normal numbers represented within toy system. any one knows how to solve this question?

[mehrdadtoofan]

Second example given is totally wrong!
010010 times two to the power of three is 12.5 ( don't forget the hidden one) and also the twos complement value of 100100 times two to the power of two is minus 3.5 (again don't forget the hidden one) . When you add these two, the correct answer is 9 and not 1 as the video says. The error is where the intstructor should shift the second number to the right (and not to the left as proclaimed by the video) to be able to increment the exponent.

At any rate the correct result after the addition for mantissa is 000100 and for the exponent 0011 which are the same as what he gets but have a different interpretation!!