Binary 3 - Fixed Point Binary Fractions

[@callumbarker3190]

Very helpful and informative compared to my teacher's website when trying to revise for mock exams :)

[@ComputerScienceLessons]

Glad to help. Perhaps your teacher would find my videos useful :)KD

[@lumennganje2721]

you are so good you should start a series on android programming

[@jccab]

At 4:04 , why does it start with -1, followed by 0.5, 0.25, 0.125? Is it because of the two's complement for 4-bit registers?

[@hmac_sha2569]

Thanks for the video, helped me a lot

[@ComputerScienceLessons]

You're welcome :)KD

[@BoraY5734]

in 4:27 why is the number before binary point -1 and not +1

[@forgedynasties]

Because it is following the 2's Complement notation i.e MSB is always a weight of -2^n

[@Agilitynitro]

at 3:37, The middle equation, isnt that suppose to be 1100 after binary point (55,75)?

[@ComputerScienceLessons]

No. -128+64+8+0.25 is 55.75 You need to bear in mind that we start with a negative place value. Therefore to arrive at a fractional part of .75 we need to add just 0.25 to -56

[@Agilitynitro]

Thanks for clearing that up! Went over it now to see what I was thinking and I did not catch the part where it decreases in place values. You're very clear and detailed in your explaining so I want to point out the obvious that it's just me being dumb and not you, thanks a lot for these useful tutorials, these are the best one out here!

[@ComputerScienceLessons]

It's important to question everything. I'm glad you've now seen the light. I tell my students to show their working clearly in an exam; if this is sound, the examiner will usually forgive small arithmetic errors. Thanks for the kind comments, and for keeping me on my toes.

[@boudieraurelien8531]

@@ComputerScienceLessons Thanks , i did the same mistake, it's all right now, i understood!

[@icebeardoesnttalkmuch8919]

just one question! if the denary number given to us is negative with most significant bit as 1 then do we need to take the 2's complement of the rest of the integral part ?? or do we convert into binary without any complement?

[@ComputerScienceLessons]

Fixed point binary is an alternative to two's complement. If you are asked to express a denary number in FIXED point binary, then two's complement is irrelevant. Just assume everything is positive when you do your conversions then change the left most bit to 1. If the left most bit is ALREADY 1, then the magnitude of the number is too big to used fixed point notation.

[@icebeardoesnttalkmuch8919]

got it! a bundle of thanks ..

[@rhythmandacoustics]

There is 2 things I learn when watching this video. First is how to do the process and the second is how different terms they use in UK compared to North America. Denary = Decimal, Vulgar Fractions = Improper Fractions. But it appears he uses the terms ZERO and NULL (pronounced by the BRits as Nord)

[@ComputerScienceLessons]

I prefer 'Denary' to 'Decimal' but most English people say 'Decimal'. A vulgar fraction is any fraction written as a numerator on top and a denominator below (E.G. 1/2 instead of 0.5 or 3/2 instead of 1.5). An improper fraction is a vulgar fraction in which the numerator is bigger than the denominator (E.G. 3/2). Zero is the number 0, but NULL is the complete absence of a number. I sometimes use the word 'nought' (as in 'noughts and crosses') instead of 'zero'. :)KD

[@rhythmandacoustics]

@@ComputerScienceLessons Interesting. Neve heard of "noughts" in North America. I have always thought of NULL as Zero , because NULL in German means zero, as is Hunde i hound or dog. Thanks for the insight.

[@MrMeeseeksPiano]

and why couldn't I represent -55,75 as 11001001.1100?

[@ComputerScienceLessons]

If you were a processor designer, you could design one to do just that. However, when working in two's complement, you would typically add the fractional place values to the overall total. Hence 11001001.1100 becomes -128+64+8+1+0.5+0.25 = -54.24 You will need to do it this way if you plan to learn about floating point binary next,

[@anonymouscode1616]

Bro why you keeping '-' on the end of 128 bro Pls reply me bro

[@ComputerScienceLessons]

These values are stored in registers. The leftmost place value is considered to be negative by the processor. :)KD

[@anonymouscode1616]

@@ComputerScienceLessons the left most place will consider as negative in all device

[@aycayldran8248]

@@ComputerScienceLessons but we added - when the beginning just 1 in floating point. What changed?

[@Stupoider]

I converted the real part of -55.75 to binary using the long division method and keeping track of the remainder which gave me 00110111. If I flip the bits, I assume that's how I get -55. After that, I tried calculating the non-integer part using the long multiplication method and keeping track of the real number result - this gave me .11 for the non-integer part, which doesn't quite match the answer even when flipped. I'm assuming the method I'm using can't be applied to negative integers the way it applies to positive - but I suppose this is all easily solved if I just use the place table method instead. Another thing that confuses me is when a question says "Using two's complement", because my understanding of two's complement involves flipping the bits and adding 1 to the LSB - but that doesn't seem to entirely apply here either.

[@ComputerScienceLessons]

The flipping bits and adding 1 method is problematic. You would need to look at the whole number part first and recognise that your starting point is -56. (11001000) Then you need to work out what fraction you need to add to it to arrive at -55.75, namely 0.25 (.01). I think the best approach is to use a place values table. :)KD

[@mhda-c9m]

أحسنت حياك الله شكراً لنشر العلم

[@ComputerScienceLessons]

شكرًا لك :)KD

[@unknowndude0074]

Doing this in my mock exam. Question: What is the bicimal representation of the decimal number -15.625? Answer: -1111.1.1. How? Your method gives me something completely different.

[@ComputerScienceLessons]

With 8 bits to play with, positive 15.625 is 01111.101 in fixed point binary. The left-most bit is then changed to 1 to indicate it is a negative number. Has a zero been swapped for a point in your anwser?

[@abdullateefjabasa1656]

How amazing you are!

[@ToanPham-wr7xe]

😮