Tom Lehrer: New Math

[@kate251144]

I was introduced to Tom Lehrer around 1954 by my uncle, who'd lived in America, and brought back the LP. I was hooked, even that young - I was 10. I'm now 70 - something and still love him. This is a VERY clever video! Congratulations!

[@THECONTINENTALMAN]

lehrer is still alive today!

[@scubadiva666]

@@THECONTINENTALMAN Right-in his office up at Hahvid.

[@nothosaur]

To make this even more impressive, realize that Tom is playing the piano accompaniment throughout this performance.

[@scubadiva666]

I always felt David Pogue was mega-influenced by Tom Lehrer. kzbin.info/www/bejne/eoG7fKV7m7yqj9U

[@GillianGrissom]

Fun fact: I actually understand what numbers in Bases other than Base 10 thanks to this song.

[@marshabrown5760]

Me too. Once helped a kid cousin who had to learn it, and was able to because of this song.

[@billybbob18]

I prefer base 1 myself... Im lazy.

[@LocalMaple]

@@billybbob18 Base 1? That’s nasty. Four would be written as 1,000.

[@joshualeong7894]

How many fingers are you missing?

[@THECONTINENTALMAN]

​@@joshualeong78942, probably.

[@starponys0740]

The purpose for having students "think" about math is so that they understand how and why the efficient algorithms work. The purpose for "learning math" in the first place is to become a human calculator. The two extremes to avoid are (1) the blind learning of algorithms and (2) the eschewing of the most efficient algorithms. The purpose of "reforming" math lessons should be to make the proofs for the algorithms as lucid, concrete, and intuitive as possible. This is what I try to do.

[@Storel79]

I played this for my father once back in the Seventies, and he cracked up when Lehrer got to the line "if you're under 35 or went to a private school you say 7 from 3 is 6, but if you're over 35 and went to a public school you say 8 from 4 is 6." My dad was over 35 then but had gone to Catholic school whereas my mom had gone to public school, so apparently he knew EXACTLY what Lehrer was talking about there! 8-)

[@bryantchang1007]

I still don’t get this can anyone explain please

[@drmsanford]

@@bryantchang1007 It has to do with moving the 10 units to the one's digit. 342-173 can be written as 300+40+2-(100+70+3) one algorithm for subtraction is to subtract 10 from the 40 and move it to the 2 so you get (300+30+12)-(100+70+3) so you can subtract 12-3=9. In another algorithm, you take the 10 from 70 but since 70 is necessarily negative it looks like you add (300+40+12)-(100+80+3) so you get 12-3=9. But, notice that in the first algorithm the upper number's tens digit decrease by 1 while in the other algorithm lower number's tens digit increases from 7 to 8. I had students from Africa that subtracted the second way while most of my students do the first way.

[@bryantchang1007]

​@@drmsanford Never would have expected a reply many months later but it finally makes sense thank you so much !!

[@thomfisher1100]

Reminds me of a recent argument I had with my daughters math teacher after I read her math book! Quite a discussion since I am old school engineer. Great video BTW!

[@jiggyjigster1117]

7 titles at the Tour de France

[@אנייהודי-פ4ט]

EMMET bo burnham fans around the world applaud you

[@celiamass]

Started watching the TED Talk Periodic Elements videos and that led me to Tom Lehrer and that led me to New Math. Ah....those/these are the days. Thanks.

[@jarethjohnsoncomedy]

Well done!! I'm old enough to remember this, and have the 12 inch vinyl record!

[@5up3rp3rs0n]

*Only if the fraction part existed....*

[@dhrousseau]

This video single-handedly taught me how to do math in different bases over a decade ago. Thank you for your service, and ht to Tom Lehrer for creating this song, of course

[@Thatwasademo]

basically, "1"+"1"="11" but only because when working with strings + means concatenate not add, since it doesn't make any sense to add strings: what does "8"+"quotation" equal? well, obviously: "8quotation"

[@HalfWiccan]

Am I the only one here who thinks that he looks like the Engineer from the TF-2?

[@gamerzombiesblandston2111]

Kinda

[@paulluna8099]

He did work on the Manhattan Project before going into music.

[@paulluna8099]

Tom Leher did anyway.

[@Err0Rose]

holy shit he does

[@captainjirk9564]

Especially with the bad lipsync lmao

[@haltersweb]

I guess this new math is now old math because this is how I learned to do subtraction in the late 60s. Just looked it up and this song was from 1965 so this makes sense. I wonder what NEW new math method my kids were taught in the aughts. I need to ask them.

[@MorganBennett]

You can't take three from two, Two is less than three, So you look at the four in the tens place.Now that's really four tens So you make it three tens, Regroup, and you change a ten to ten ones, And you add 'em to the two and get twelve, And you take away three, that's nine. Now instead of four in the tens place You've got three, 'Cause you added one, That is to say, ten, to the two, But you can't take seven from three, So you look in the hundreds place. From the three you then use one To make ten ones... (And you know why four plus minus one Plus ten is fourteen minus one? 'Cause addition is commutative, right!) And so you've got thirteen tens And you take away seven, And that leaves five... Well, six actually... You can't take three from two,Two is less than three, So you look at the four in the eights place. Now that's really four eights, So you make it three eights, Regroup, and you change an eight to eight ones And you add 'em to the two, And you get one-two base eight, Which is ten base ten, And you take away three, that's seven. Now instead of four in the eights place You've got three,'Cause you added one, That is to say, eight, to the two, But you can't take seven from three, So you look at the sixty-fours... From the three, you then use one To make eight ones, You add those ones to the three, And you get one-three base eight, Or, in other words, In base ten you have eleven, And you take away seven, And seven from eleven is four! Now go back to the sixty-fours,You're left with two, And you take away one from two, One, that's right.

[@robin888official]

This legitimately introduced me to this song and subsequently the works of Tom Lehrer in general years ago. It's possible I watched this close to it's publication 14 years ago.

[@KoreiXume]

This is one of the best video I've ever seen. Our maths teacher showed us this video. Its soo good. Great job!!!!

[@scubadiva666]

"Base 8 is like base 10…if you're missing two fingers." We used to play this record before school every day in my 4th-grade class.

[@PeggyKleespies]

I grew up listening to Tom Lehrer! This is great!

[@SueK449]

Awesome video! I remember listening to this as a kid and just having my head spin. thank you for making me laugh like a kid! Well done video. thank you!

[@dougmontgomery1868]

I always had trouble doing subtraction--and even addition--the way we learned it in grade school, in the Fifties. Then I got a book titled _Mental Magnetism Course_ by Harry Lorayne in 1969. I learned new techniques for arithmetic altogether! I still know the basic arithmetic addition and multiplication tables I learned as a kid. But Lorayne's techniques for addition, subtraction, multiplication, and division are so easy; and calculators help--though, believe it or not, there is some arithmetic I can do that works out better than my vaunted multigigabyte desktop computer can do it!!

[@zapped56]

I actually bought this LP in 1965 when it came out. Laughed my ass off just watching your video. Excellent performance. Tom would be proud.

[@lpittleman]

bs'd Hey zapped56! Love that Barry Miles on Poppy. Thanks for posting it. Unfortunately the last track - New Derivatives - is missing the last 20 seconds. Could you repost the complete version? Thanks, l

[@georgegoss1]

Well done. Tom Lehrer would be proud. :-)

[@pecaeout]

My math teacher showed me this

[@Monosmith]

This video has inspired me and I am currently trying to figure out a way to make a song that contains similar stylistic elements to explain the proof converting ax^2+bx+c=0 to x=[-b-+(b^2-4ac)^(1/2)]/2a. Wish me luck on that. Meanwhile, this easily one of my favorite videos on KZbin. I'm not easily swayed to bestow such honors because I know that they never mean much, but in my mind this has the makings of a classic. I hope to show all my friends in Calculus this video.

[@jlang]

Luck! Did you write the song? :) You have a brilliant idea. :)

[@juliarae79]

4 years ago my math teacher showed this to our class!

[@DerNesor]

Our analysis professor showed us this in the very first lecture in 2012... It left a mark

[@Calbeck]

Great expressions and spot-on lipsynching!

[@diecastcarboss6192]

I'm going to show this to my math teacher

[@DrDerp42]

I did not grow up with this, but I appreciate the humor.

[@captainzorikh]

This is mu favorite video of this song. I am sorry you stopped making videos. This is brilliant!

[@NortheastBreeze69]

This makes me feel so old

[@arch3223]

Old math confused me so much that I tried to figure it out. A half hour later, I think I can do it.

[@timbeauregard4809]

Greetings. This song is fantastic, and I think it was made in 1965. You did a great job memorizing it and performing it. Some of the facial expressions were priceless.

[@jilow]

@TheShadowsLotus Another way to think about it in base8. There's the 1's place which goes up to 8, before rolling over. so the number 10 would represent 1. 8 or 8. 20 would represent the number 16 or 2 '8.s The 3rd slot would only roll over once it has 8 "(8s) so 100 would be 64. that would only roll over once you have 8 of those. So each place is essentially multiplying by 8 to move one over. Just like in base 10 you multiply by 10.

[@emaciasify]

Dude, way wicked. My kids love it. Keep up the craziness. We need more mathematicians to be wacky and have fun!

[@AnonymousJayne]

As someone who was raised in the years between "old math" and "new math" I totally understand what he's getting at. Online math courses are just as bad. Even my math teachers don't understand the question sometimes!

[@jamescloninger2666]

@Monosmith: This video has inspired me and I am currently trying to figure out a way to make a song that contains similar stylistic elements to explain the proof converting ax^2+bx+c=0 to x=[-b-+(b^2-4ac)^(1/2)]/2a. Wish me luck on that. Too late, Tom Lehrer already did a "Quadratic Song." ;) I think it's here: Tom Lehrer - Maths lecture (1997)

[@ImAnotherFreak]

I remember learning this in school back in first grade and it SUCKED. But looking back on it now, I'm pretty sure this video would've helped me a lot more than anything my teacher said :P

[@jack002tuber]

Now do it again in base 16!

[@phm1991]

psh naaa, base 100

[@david2869]

+jack002tuber You can't take three from two, two is less than three, so you look at the four in the sixteens place. Now that's really four sixteens So you make it three sixteens, regroup, and you change a sixteen to sixteen ones, And you add 'em to the two and get twelve, which is 18 base ten, And you take away three, that's F. Now instead of four in the sixteens place, you've got three, 'cause you added one, that is to say, sixteen, to the two, But you can't take seven from three, So you look in the two hundred fifty-sixes. From the three you then use one to make sixteen sixteens and so you've got thirteen sixteens, which is nineteen base ten, and you take away seven, And that leaves B... Well, C actually, but the idea's the important thing. Now go back to the two hundred fifty-sixes, you're left with two and you take away one and that leaves one.

[@dovbarleib3256]

New math failed because while many students understood what the 8x8 place was, the next highest digit was the 8x8x8 place. Now who can tell you what 8x8x8 is off the top of their head?

[@EscChaos]

If you're actually computing 8^3 in base ten then you've missed the point of working in base 8 already. You can keep converting back and forth between 8 and 10 like and idiot scrabbling notes in the margin of your paper but it will only work to a point. If your problem is easy you'll reject new methods and chose to work with your old tool set regardless of whether it's practical or not but by continuously scaling the difficulty curve you'll eventually no longer be able to use your old tools and you'll learn the new ones. This is how you learn anything ever but if your teacher doesn't want to give you harder problems because you're obviously having trouble with the simpler ones (really) because you're using the wrong methods or viewpoints then you'll get stuck on simple problems and never progress.

[@finnflaherty8704]

in base eight, it would be written 10x10x10, and the answer, 512 in base 10, would be written 1000

[@TheTiffanyAching]

Base 8 (octal) is still used in Unix and Unix-like operating system to set file permissions. Base 16 (hexadecimal) is frequently used to express numeric values for colours on Web sites. Both systems are shorthand for base 2 (binary), which is how data is represented on computers. Our system, base 10 (decimal) isn't a good shorthand for binary because ten is not a power of two. As Calvin might have said, I'd explain it further, but there's a lot of math.

[@Anonymous-df8it]

I'll return the question: Who can tell you what 12x12x12 (in base 8) is off the top of their head?

[@cras17]

@VinuVonVin My point was that in our numbering system a base 8 system is not intuitive. It isn't because we are just used to base 10, it is because the way we talk about numbers is inherently rooted in the idea of 10. We have 10 unique digits that repeat every 10 numbers, then every 100 numbers, then every 1000 numbers etc. The only way a base 8 numbering system would be as intuitive as base 10 is if the numbers 9 and 0 did not exist and there was a switch every 8 numbers.I say we stick with10

[@KorrinBelle]

The way we count normally is also called Base 10, because that counting system has 10 digits, 0-9. Base 8 is similar, except the digits are 0-7, so instead of writing 8, you bump up the "10s" place (or the 8's place, in this case?) So 8 would actually be written as 10 in base 8. It seems weird at first, but most people are also used to Base 12 without even realizing it. It's what we use to tell time.

[@baylinkdashyt]

I always whip this out... The clip, silly... When someone goes on about how they don't understand Common Core math. These are usually people too young to understand that what they *know how to do* was already "the new math"...

[@FALLINGCORN]

omg this video brings back so many memories XD

[@15Smartie15]

I hate how they are saying you need to know what you are doing. No, you just need to know if what you are doing will get you the right answer. It's math, all that matters is the answer. All you really need to know is what formula, if you will, to use in any situation.

[@themovies234]

I'm still confused...

[@sixfingr]

Love Tom Lehrer. Nice job. Very entertaining.

[@MindControlArtist]

Easily one of my favorites. LIsten to the whole thing.

[@sweeneykelley]

For all my friends who had trouble with the OLD math.

[@ui0ekim52]

@lipsynchorswim The answers are different in Base 10 and in Base 8, because the starting numbers represent values that are fundamentally different. You can indeed verify that 147 (8) = 103 (10).

[@DxXNA]

Might as well switch to base 16.

[@jrstf]

That would suck, we have 6 too few digits.

[@claudiamastroianni4300]

A-F work just fine.

[@jrstf]

If I write FAD the computer may have trouble figuring out what I'm trying to say. That's why, with computers, we don't use the letter O as zero like we did 70 years ago with manual typewriters. I know you can do strange things like write 0xFAD but it would be a whole lot easier if the set of digits and letters did not overlap.

[@felipevasconcelos6736]

Seximal (AKA senary, AKA base six) is the superior base. The first integer inverse that’s not very simple in seximal is one elevenths, all previous ones are terminating or have short periods.

[@timbeauregard4809]

oops, I hit enter too soon. Just wanted to comment on the above comment and your reply. They are completely different values to start off with in base 10 and base 8. The "process" of subtraction is the same, but since you start off with different values, the result is also different. Base 10: 342-173 = 169. Base 8: 342-173 = 147. 169 in base 10 is not the same as 173 in base 8. 173 converted back to base 10 is 123, and 169 does not equal 123.

[@kin2naruto]

I learned both ways. Or rather....my teachers attempted to teach me using every method they could think of. Nothing stuck until I hit algebra - and then math made sense! I probably laugh a bit too hard at this song.

[@softy8088]

@abebou 12 is interesting in that we actually have natural English words for powers of 12 (up to 12^2 at least) which we don't have for the other bases (except 10 of course). Consider "eight gross eleven dozen and ten". Using "A" for ten and "B" for eleven this is 8BA (base 12) = 1294 (base 10).

[@Negi2468]

@cras17 The point is not to work in Base 8, it's to work in an arbitrary base. Base 8 is just an easy base to work with.

[@1metalnation]

@lipsynchORswim hex is actually a way of binary conversion, all computers at their very roots run in base 2, as you mentioned, hex just takes all those lines of 1 and 0s and turns them into something slightly more manageable

[@PlasteredDragon]

@cras17 most of the low level computing languages do arithmetic in base two (binary), base eight (octal), and base sixteen (hexadecimal)... if you were going to do some coding in ForTran back in the 70's for example, you'd need to know your octal. Octal is a useful way to express 8-bit values. Anyway, you can do whatever base you want. You simply select your digits and columns on that base. So base 5 has 5 digits (0,1,2,3,4) and columns in powers of 5 (1's, 5's, 25's, 125's) etc.

[@raydredX]

I found myself reading your comment to the song's rhythm even though it was over... Anyway, that's normal for "new people", I even think the "new math" should be even "newer". But this is coming from someone who'd happily study maths at university if he could, so...

[@paulrank]

A bit is a bit. I intended to show that we were using a 1,000 octal bit - that is, a physical matrix of ferrite cores that could be polarized in 2 different ways that was constructed to respond to octal arithmetic internally - memory. This was a cubic structure about 5 inches on a side, weighing about 2 pounds, made mostly of iron! We numbered each bit within the core with its octal address. Enough said.

[@larryyoung8039]

I learned new math and am just beginning CC Math with my kid. Paul Simon was right "When I think back on all the c**p I learned in High School, it's a wonder I can think at all..."

[@Avyncentia]

This is brilliant lip-syncing. Great job! Also, great song!

[@paulrank]

I actually had to use Base 8 when studying early computer structures and programming. In fact, we manually input data in the ferrite core of our Univac Digital Trainer, which had 1,000 octal bits, or 512 decimal bits, of RAM that we had to address individually to input to the various registers. Our output device was a teletype writer, and we input the data by pushing binary coded decimal groups of lighted switches to change the states of the octal bits. Not user friendly...

[@SupermarketSweep777]

I grew up with this in the 90s before all this common core crap, and it's a cakewalk in comparison.

[@theendofit]

This audio is from 1965. So no hes actually complaint about how you were taught. Congrats on proving that common core is just as normal and logical as the math you learned

[@Wolfrover]

@TheShadowsLotus We have a hundreds place because ten tens is 100; in base eight (which is useful in some computing languages and other mathematical alleyways), you'd have a place for eight eights, and eight eights is 64. (He explained this in the song, you know.)

[@jbylin]

This is great. It’s visual. Definitely will show to my kid who is just about old enough to comprehend base 8. I wonder if Professor Leherer knew how important base 8 calculations would become…. When I see 12 I still think C.

[@constancesmith4015]

So funny...this guy reminds me so much of a young Arlo Guthrie!

[@racoonknux49]

The idea is that nobody in the audience grew up with it, unlike you. Leherer capitalizes on this and comedy is produced as a result. As an example, I was taught math the "normal way", and as a result I am able to appreciate this for its comedy value.

[@minime1235able]

@lipsynchORswim Incorrect.... Take the example: 100 base 8 - 0 base 8 = 100 base 8; 100 base 10 - 0 base 10 = 100 base 10. 100 base 10 != 100 base 8. They are different numbers before hand, so you will get different numbers afterwards. If the problem was to give the answer in base 8, you could either change the operands to base 8 _before_ or the sum _after_, getting the same answer because you are still using the same numbers.

[@deltasr5443]

Bloody hilarious and ..... awesome!!!!

[@abebou]

I like base 12. Which is what our measurement of time is based on, btw.

[@sagbag]

@Menarkh Oh! So 'new math' is just writing out the steps rather then doing it in your head and writing it down. That makes sence, thanks!

[@AnotherSpecialEdMom]

@ChaoMystero it is and was confusing. I maintain that this is why I still do math on my fingers (50+ years later). The way he presents it here is exactly the way it was presented in the classroom. :)

[@CrabTastingMan]

@lipsynchORswim "Base 8 works in a similar fashion to base 10 (which most of us are used to)" speaking of familiar number systems, I hear some people in central american used base 20.

[@MathTine]

@JH9234 sure, it could work, and it does work in a lot of cases. Problem (at least here in the Netherlands) is that if a kid does not understand it, you lose both things: the pupil cannot add, and doesn't understand. If you go with the old method, and after that teach the theory behind it, the chance that a pupil can at least perform the arithmetic is much better. Of course, I do agree that a good method should also teach understanding.

[@6or1]

I don't have enough fingers and toes to count on.....

[@leftofzen]

@paulrank: Last time I checked, a bit is a bit, there is no such thing as a "decimal" bit or an "octal" bit, since a bit is a single quanta of data in a binary system. So a bit can either be on or off, true or false, 1 or 0. So not sure where you are getting decimal/octal bit from. Even if you meant byte, that still doesn't make sense.

[@carultch]

Use plus as concatenation of strings, with caution. I've worked with numerous platforms where that operator isn't set up to work that way. It is immensely frustrating to need to search the help text for what syntax I need to use instead, for concatenation.

[@timbeauregard4809]

In the song Tom Lehrer says what's important is that you know HOW to do it and not getting the right answer. Great line, BUT, if you know HOW to do it and are careful, you WILL get the right answer. Your comment of how 100 in binary is 4 in base 10, is certainly correct, but I think the person asking the question was thinking along the lines of 169 base 10 being equal to 147 base 8. Which would mean he/she would think that 100 base 2 would be equal to 100 base 10.

[@oniyaajila]

40 people are still waiting for fractions

[@karenq3320]

Still love and appreciate TL’s weird sense of the absurd.

[@asphodelale]

This explanation of subtraction makes perfect sense if you use an abacus to illustrate--every bead on a given wire equals ten beads on the wire to its right, if working in a base 10 system. If you un out of beads on a wire, just get rid of a bead on the wire to the left, then give yourself 10 more beads on the original wire. Easy as changing a $10 poker chip for 10 $1 poker chips, and the same principle. Of course, one can also make abacai to represent other bases, just by using different numbers of beads on the wires. (One could, theoretically, even make one that'd be able to calculate galleons, sickles, and knuts.) Point is, the new math isn't so complicated, once it can be visualized.

[@LadyeXo]

I adore your voice. When I heard the "Masochism Tango" I about died.

[@RedwoodTheElf]

And this was (more or less) a joke song when written. but now we have Common Core where (as Tom Jokingly said) the important thing is to know what you're doing rather than to get the right answer. I weep for the future.

[@cras17]

Who would ever do anything in a base 8 system? That is totally counter-intuitive to our entire number system. He did have a good point in there though. The idea is to understand what you are doing, not to get the right answer. He said it sarcastically but that actually is and should be the focus of learning math.

[@nettiespiwack7586]

I never recovered from New Math. When Common Core was introduced, all I could think was: "they never learn".

[@joshuachesney7552]

Yeah, its just that I had come to think that new math was something we tried for a while before giving up on and discarding entirely. It never occurred to me that some of the concepts might have stuck around and gotten into canon math teaching. That is why I was confused.

[@Strill_]

@Ziiiv Personally I think trying to teach rigid exact mathematical concepts using the vague English language makes things far more difficult. It's much easier to understand math when you have an exact algorithm to study which conveys things much better than trying to figure out what someone means when they talk about abstract concepts I can't relate to and explicitly avoid using metaphor.

[@PersephonesFear]

@cras17 While my schools could not understand 'why' I was so far ahead of my peers in multiplication, division, math, etc (because I did math drills, could 'guess and check' fast, elimintate wrong answers quickly, memorize formulas, etc) - they thought it horrible that I never showed my work. The schools loved 'mental math' - making us spend 4 pages showing 'two different ways, with graphs' showing how we arrived to the conclusion of a given word problem. (It didn't matter if we got it right.)

[@Jetpower485]

This really needs to be animated in School House Rock style. And for those of you wondering why on earth do this like this, it's necessary for PLC (Programmable Control Logic) programming, but I don't recommend trying it on a 2nd graders first. Save it for 5th grade!

[@swistedfilms]

I was introduced to different bases in 5th grade but I think the one concept that the teacher didn't introduce, and one that I didn't deduce myself, is that the idea of the next place in line being an exponent of the base, whatever that was. I think if they had explained that 64 was the square of 8 at the time, as Professor Lehrer did here, I might have grasped the concept easier. But I just couldn't wrap my head around it at the time.

[@andrewmihovich4252]

Everyone's aware that this was originally recorded in the 1960s, right?

[@carultch]

No, by definition. In base ten: 342 = 3*hundred + 4*ten + 2*one 173 = 1*hundred + 7*ten + 3*one 342 - 173 = 169 In base eight: 342 = 3*sixtyfour + 4*eight + 2*one = in base ten 226 173 = 1*sixtyfour + 7*eight + 3*one = in base ten 123 342 - 173 in base eight = 147 in base eight, which is 103 base ten 226 - 123 in base ten = 103 base ten Neither of these equal 169 base ten.

[@Yonkage]

This guy should have been in The Matrix.

[@joshuachesney7552]

A reasonable point. I was just baffled because I always heard that New Math didn't work well and was eventually thrown out. Then I learn that "New Math" is the way I learned to subtract. That was kind of confusing to me. A bit of a contradiction to what I had always thought.

[@carultch]

@KXMelodyKX Yeah, but the people who made up our base ten counting system didn't have different words for fingers and thumbs.

[@ChevaliersEmeraude]

@YouDuck2345 Well, you do have the base of the concept right, thought. Base 4, for instance, would be counted as 0, 1, 2, 3, 10, 11, 12, 13, 20, 21, 22, 23, 30, 31, 32, 33, 100, 101, 102, 103, 110, 111, etc. See, 100, here, is the same as 16 (or 4-square) base 10. So yeah, you had the bases of the system right. But you can't just divide and multiply to change the base 4 to base 10, Truth be told, unless you're used to a system, it can be hard to switch any large number from any base to base 10.

[@carultch]

Uh, did you not watch him go through the arithmetic steps? Let's start at the top. You can't take 2 from 3, 2 is less than 2, so you look at the 4 in the 8's place. Now that's really 4 eights, so you make it 3 eights, regroup, and you change an eight to eight ones/ You add it to the two to get 12 base eight, which is ten base ten, and you take away 3 and that leaves 7.

[@WytZox1]

* It is important to know binary (base 2) & hexidecimal (base 16) in computer science! ☺

[@artax84z]

That's funny, I was not that great in Math and was always in the basic math classes. When I had completed the Math requirement I didn't know what to take as electives, so I took Pre-Algera and got A's, then I went on to Algebra and got A's and B's. That's when I understood it. Have not thought about it for years and just looked at a few old math school papers I had. It was an A plus but looked like it was in Cantonese. Don't know how I got an A.

[@Milehighyena]

That's how I was taught to do math though. It makes more sense than what he was doing in the first part...