Summer of Math Exposition

Presented by 3Blue1Brown 3blue1brown

Computers Do Not Add & Subtract Like Us!

Audience:

Tags: binarylogic-gatestwos-complement

Discusses how computers use the binary system to represent number and perfrom arithmetic on them. Also covers the two's complement and how it can be used to represent negative numbers and the way adder/subtractor circuit can be built from logic gates. Audience is everyone, but mainly high school and undergraduate students.


Analytics

5 Overall score*
120 Rank
13 Votes
9 Comments

Comments

5

This video is clear as well as a good lesson about binary system and computer calculus, but it doesn’t offer different approaches or remarkable techniques of memorization.

6

The first 30 seconds of the video are just a blank screen. Put something there! The voice-over was quite nice, but I want to see something, too!

6.5

You have a very nice explanation of two’s complement. You covered a lot of ground in this video, so I’m a little worried if this will go over the head of people that have not considered binary or logic gates before. Maybe it would be nice if you addressed some loose, but interesting ends: why do we have to use an adder as a subtracter? Why did we make a full adder by string together a bunch of 1-bit adders? What happened to the orange 1 during the two’s complement explanation?

6

I think a beginner could follow the video which has good rythm and it’s quite clear. Since it’s focused in circuits and operations it ‘s posible that non-familiarized students with binary system get a bit lost in the introduction, because I feel It like a non exhaustive sum up. Maybe a more visual explanation with the classic “balls and boxes” approach would have been nice, not comparing decimal and binary numerically but logically because 8,4,2 and 1 appear in some way out of nothing for students who’re not related with the conception or powers of ten in decimal number. I know in some way this is a “primary school Matter” but I really think that a lot of students haven’t give a thought about this so focusing in It for a bit would have been great. For the rest, the circuits and diagrams were so clear and understandable. Also the imagen. Maybe try to Focus on recording and editing audio and care for the little wistles and breathings if you have time for It. Congratulations!

5

The “ticker” animation at 1:29 is very good and intuitive, and colouring the wires green and red is a good idea. It would have been nice to mention why computers use binary at the start.

At around 6:08, it would be nice to go a bit slower and explain the intuition/english behind these gates. The information dump at 6:42 is a bit too much - I think this could have been improved by guiding the audience along a discovery of this adder, rather than assigning them homework to check that it works - they gain no insight.

The twos complement explanation is really clear and I like the colours - it would be nice to motivate it though, for example at around 11:30, showing that if you add the twos complement to the original, the “invert all bits” step means you get 111…1, then the “add 1” step tips it over the edge.

8

Great video! The video I submitted for SoME this year was also focused on 2’s complement, although I’d say I like yours more :) You did a very good job connecting from one topic to the next and showing an intuitive explanation of why two’s complement works with decimal, and using the circuit to show the benefits of performing subtraction this way. If I had to offer one suggestion, maybe you could add one more step between binary addition and logic gates, showing a table of inputs and outputs to make the function of the adder a bit clearer. Overall great job!

Fun fact from my video you may find interesting: the process of flipping bits and adding one also works in a base ten system. To flip a bit in decimal, you just subtract it from 9, so 0 swaps with 9, 1 swaps with 8, and so on. So for the example you gave in your video around 10:10, 34 would flip to 65, then you would add 1 to make it 66

3.2

This is a very clear explanation of the way computers add numbers. Unfortunately it is a little dry and will probably fail to hold students attention.

The video does not use any animation or graphics which could hold the viewers attention.

5.5

0:00 Please put something in the screen just so people aren’t wondering if the video is broken or smthn. A title or logo or anything would do really, though something also giving an idea of the video, like operations or an image of a calculator zoomed to the operation keys, would be better.

1:35 These numbers should really be right aligned, especially since we are just explaining how to place digits in binary.

In general if you want this accessible to more advanced students like high and undergrad, you should offer a way to skip the explanation of binary numbers since that’s quite common knowledge and takes up a lot of time here

5

Yea! The pacing does feel right.