Binary to BCD (Double Dabble Algorithm) - Computerphile

Double it and Dabble where required - The neat trick that turns pure binary into binary coded decimal. Professor Brailsford performs the magic!
The Professor's Notes: bit.ly/C_DoubleDabble
C.B. Falconer's Notes: bit.ly/C_cbfalconer
42 & Binary Coded Decimal: • Binary Coded Decimal (...
EXTRA BITS: • EXTRA BITS: Double Dab...
/ computerphile
/ computer_phile
This video was filmed and edited by Sean Riley.
Computer Science at the University of Nottingham: bit.ly/nottscomputer
Computerphile is a sister project to Brady Haran's Numberphile. More at www.bradyharan.com

[@FourthDerivative]

And when the nibbles double dabble with a paddle in a bottle and the bottle's on a poodle and the poodle's eating noodles, they call it a poodle noodle bottle nibble double dabble muddle.

[@Tehom1]

That's enough, sir. I can't say such silly stuff, sir.

[@bensmith9253]

Ha! You got me so worked up with that comment I held me finger on the like button to try to "love heart" it! Lol

[@fromatic2]

Ded

[@stocklilves4060]

FourthDerivative xD

[@thebullybuffalo]

Ok dr Seuss

[@THEROTATINGFOOT]

I've wondered how binary gets converted into decimal efficiently for a while. I've come across BCD but never got into the actual algorithms for conversion. Great answer to a question that I forgot I had!

[@SuperU2tube]

Been a programmer for more than 40 years and fully understand both binary and decimal and binary coded decimal and yet this video makes something simple look complicated!

[@SE45CX]

You have developed your own approach to the matter and verified this with the software you wrote countless of times. In the video you must follow this guys take on the subject, which is unfamiliar for you.

[@chipacabra]

One of these days, I would love to hear Professor Brailsford talk about Big Endian and Little Endian representations of numbers.

[@CarzyNavi]

I love the fact that they always use the retro printer paper in every video... what a good use of outdated stuff... XD

[@sebastianelytron8450]

I'm a simple man, I see a Prof Brailsford video, I break the laws of nature and the speed of light with how fast I click.

[@oZed696]

I´m a simple man.. Yup, that´s about it, just simple. This is breaking my brain.

[@NeilRoy]

Always a pleasure to listen to him. Never a dull moment, at least for me.

[@JoseTorres-tr6od]

It works because 2*5 > 10 so any number greater than 4 will not carry correctly after the shift (x2). Suppose 4

[@ShipOfFreaks]

should clarify that you only add 3 *if there are still shifts left to do*. if on the last shift you get values of 5 or greater that's fine.

[@aidywady4553]

You explain this very well. Thank you for the video🙂

[@Controllerhead]

Thank you for explaining this magic. Helpful for 6502 NES programming with no BCD mode!

[@MePeterNicholls]

I love how binary is efficient and minimal.

[@joshsmit779]

I really needed this 3 months ago:(

[@RobertT1999]

nicholas williams In Sixth form (which ended a year ago), I was very lucky when it came to Computer Science because the majority of Computerphile videos were uploaded a week before we learned it in school. Shame to see that not everyone is having the same luck.

[@krasorx]

Same here, 3 months to late

[@tophalfofabarn447]

I'm in the midst of a relay calculator project (8 digit, 4 function calculator) and I was originally going to use a relay decoder feeding into a diode array to brute force parallel bcd multiplication. But after watching this video I can see that to make a parallel double dabbler I only need eight +3 adders and some supporting logic, which is a much cleaner solution than 40 relays and 768 diodes. I haven't finished the parallel multiplier truth table yet, but it looks like it won't take many more relays than the full adder logic. This allows me to stay true to the relay logic design but still be able to add two eight digit numbers in 3 seconds, multiply them in 48 seconds, and divide them in a few minutes.

[@DzDesignHD]

This was awesome, thank you for showing me this :D

Great explanation. Thank you

[@jonskili]

The Thumbnail is gold

[@trucid2]

Nice shirt, prof!

[@Na0uta]

You're doing God's work with these videos.

[@SE45CX]

You know, having to make something work with a microcontroller and assembly make more sense to learn about this stuff than just listening to this guy and doing some exercise on paper.

[@bluekjar]

I love this channel..

[@travispetit2410]

Bubble Bobble

[@OrangeShellGaming]

Double Dribble

[@bsvenss2]

GOTO: Travis Petit

[@andrewrobertson1473]

AddressError Double Dwibble

[@FrankHarwald]

Tippy-top

[@FourthDerivative]

Double Dragon

[@gordoncousins5544]

Some months ago i got inspired to build a HEX game in Minecraft and in order to make it work I had to convert 8 bit Binary to 3 digit Decimal, I of course had no idea how to do this, KZbin to the rescue some very long videos later and i was able to get my head around Double Dable and build a circuit that does the conversion fairly quickly.

[@CronosXIIII]

Did a similar thing 10 years ago in Powder Toy. Displaying binary as decimal is a very common roadblock for anyone starting with electronics. Luckily the solution is quite elegant.

[@nqinadlamini]

That is one sweet way of saving machine cycles.

[@velho6298]

Brilliant!

[@etmax1]

So dabble is then somewhat miss used, because so often people might ask "do you know how to do xyz" and the answer will be "I dabble" meaning "I give it a try" or something to that effect which is not always necessarily the same thing.

[@grantnichol4496]

Whoa, I actually commented on the BCD video saying that the double dabble algorithm was useful for converting binary to BCD!

[@enceladus32]

Sounds british, but says zero instead of nought. I think he's an american spy.

[@PasqualItizzz]

Just ask if it's ok to put gravy on biscuits .... the British will instinctively recoil in horror

[@afreen5058]

I think he said nought at the beginning.

[@TheSulross]

he says Xed instead of Xee - so on that test he's an imperialist instead of a colonist

[@ozbjd]

Very interesting lecture and the shirt is cool too.

[@timoteedrimes6400]

he is doing the dabble **two times in a row**

[@n8style]

This guy's a national treasure

[@hidroman1993]

"You can go and dive in there till your heart's content" it'll be, Sir, it'll be ❤️

[@MattLohkamp]

so this method works up to 4 binary digits (15 in decimal) - can you extend it to work in 5 digits (31?) Does that just require an additional bit in the tens and units groups? is 11 (3) still the magic number to add?

[@rikschaaf]

So, from 10s (upto 16) to binary, you have to (correct me if im wrong): - shift right, - if units start with 1, subtract 3; - shift right - shift right - shift right

[@MrCyanGaming]

just remember, greater than 4, add 3

[@JmanNo42]

I guess the I/O routines in the main/computing device check for message code to send over port, but do the receiving hardware have a nibble decoder, and check the four start bits for if it is an for if it is a BDC or ASCII message?

[@hiqwertyhi]

bloody genius, that

[@jesseb6911]

the David Attenborough of computers

[@LinuxLuddite]

wish I watched this in my fifth semester college days

[@gordonrichardson2972]

Someone asked about Double Dabble in the previous video. I didn't expect that algorithm to be included in a video.

[@gordonrichardson2972]

I wouldn't call it a neat trick, its still fiendishly difficult to convert large numbers from binary into BCD! P.S. Same shirt, must have been recorded at same time, then split out from previous video.

[@killymxi]

Plz make a Computerphile video about DEC64. Interesting thing to compare with BCD.

[@jeffirwin7862]

I don't think I understand the application of this. Is the application banking? Isn't it easier to do everything in units of cents with traditional binary integers, then convert everything back to base ten at the end?

[@RedwoodRhiadra]

The banking thing is something of a red herring - actual banking applications *do* use integer arithmetic on cents. The real application, though is conversion of your binary numbers to a printable representation for a human to look at, because we expect base 10. And that of course happens at some point in nearly every program.

[@jeffirwin7862]

MichaelKingsfordGray then you just work with integers that represent 1/1000, or 1/10000, etc. If it's not base 10, then BCD won't help, but you can still work with integers in units of the greatest common factor of all the divisions.

[@Loundre3]

@@jeffirwin7862 For uC programming on a 7 segment display or any kind of display, BCD is going to be used whenever there are numbers.

[@javabeanz8549]

Hmm, wish I still had my code from college, we did conversions to BCD in 8086 ASM ( yes, actual 8086 on the Intel system development kits, hex pad and all )

[@djwaltoaram7052]

I WANT AN IMAGE OF THE THUMBNAIL!

[@SuviTuuliAllan]

BitArcher Eeww didn't need to know that

[@ootommo1]

Isn't this the exact reason the mantissa and exponent is used?

[@jeremydavis3631]

I take it you mean for storing 0.1 in binary? It still depends on which radix is used. IEEE 754 apparently allows either 2 or 10, but AFAIK, the vast majority of computers use a radix of 2. In that case, the exponent is -4, and the mantissa is 1.1001100110011... (i.e. still an infinite bit string) because 0.000110011... = 1.10011... * 2^(-4). If the radix is set to 10, of course, 0.1 can be stored with an exponent of -1 and a mantissa of 1. Also, as ManWithBeard1990 said in his comment, fixed-point arithmetic can get around this problem if you already know exactly how precise you want the measurements to be. In the example of storing U.S. currency, you can store a number of cents instead of a number of dollars. Or, if you don't mind a little overhead, you can represent any rational number as a pair of integers. Anyway, I think the main purpose of binary-to-BCD conversion (in modern uses, anyway) is to communicate a number to the user in decimal. I don't think it's feasible to try to get around that by storing the number differently.

[@johnlister]

Or: L R1, CVD R1, Included in real machine architectures since the 1960s...

[@jonathanguthrie9368]

You know, my current bank balance is greater than $0.10. It's AT LEAST $0.20!

great

[@DanDart]

If you were to try to decode 8 bits into 12 bits this way using pure logic, you'd need 1676 NAND gates.

[@frankharr9466]

Interesting. I'm not sure I understand the whys and the hows fully, but interesting.

[@Hampstead343]

By tweaking the algorithm a little, we can do any base.

[@kauhanen44]

Why don't we just learn hexadecimal... It's easier for everyone. You could even count to FF with your fingers using binary-coded hexadecimal, and you'd only use 8 fingers, leaving thumbs to hold the other fingers down conveniently.

[@potentiallyRealWarrenGraham]

I am the Globglogabgalab, I double dabble dabble double dibble double dab

[@blahdelablah]

Seems like there could be a far better way of handling this, either through hardware or software. Just use an AND gate or operation on the first and third bits of the nibble, and if the output of the AND gate/operation is 1 then that goes to both the carry pin of the next nibble and the reset pin of the current nibble.

[@hedgechasing]

blahdelablah that wouldn’t work in general. The algorithm as outlined here can simply be applied without thought to any arbitrary nibble and so it can handle converting any size binary to bcd without more thought.

[@kamosevoyan4370]

Could anyone tell me floating number representation algorithm? Please.

[@JimGriffOne]

Instead of binary, hex or decimal, my bank balance is determined by my car. British engineering at its finest...

[@brian554xx]

The professor said Falconer's Notes did not explain how they came up with it. I disagree. "The rationale for the ADD-3 rule is that whenever the shifted value is 10 or more the weight of that shifted out bit has been reduced to 10 from 16. To compensate, we add 1/2 of that 6, or 3, before shifting. We detect the 10 value after shifting by the fact that the value before shifting is 5 or greater. Notice that the rule ensures that the various digits can never hold any non-BCD values." For someone accustomed to machine code, this should be very nearly intuitive.

[@JmanNo42]

This is probably a silly question, but why would you want binary encoded decimals, is this for direct printout without conversion what is it about? Is this how the old mainframes, or even cashdrawers used it or is this still going on? Or is this going on/did go on in arithmetic circuits, i do not quite get it? I guess i ask could you give us examples for situations where the use of double dabble, how was it or is it used?

[@JmanNo42]

That is the problem for casual highlevel programmers like me we never really understand the need for the dabble going on underneath our highlevel languages, so we do not see the purpose? This is probably obvious for any assembler or machine language programmer. I would have to think real hard to see the use for it and the situations it is needed?

[@JmanNo42]

Numerical storage using base 10? If so why? I more and more seem to recall it is a cashregister thingy? So maybe base ten arithmetic in a cashdrawer printout, am i right about the use?

[@ronnetgrazer362]

I'm as confused as you are, I was hoping for a better explanation of the application, it's all so very abstract as always. And where is this? Does this go in the firmware if my device has a screen output for instance, or has this already been implemented in silica? Do I need a library for this, or does the compiler know what needs to be done? Or is this ancient tech that nobody needs anymore, because who cares about a few CPU cycles? And what happened to 3 and 4, who counts 1, 2, 5, 10? Why is doubling such a big deal, why not count with units of one? If you already need something to check if your value is 5 or higher, instead of mucking about with a shift register, why not check if the value is 9, and if so, carry over the 1 and set all the less significant bits to zero? 16 - 10 = 6, divide that by 2, so that's 5 or higher, wait, what, WHY? Why wasn't the interviewer wondering the same things, am I that thick?

[@JmanNo42]

I did look at the Falconeer example and it got a little clearer to me, it seem to suggest that somekind of hardware that do printouts "paper or screen" using nibbles, so the idea of storing nibble-"digits" was probably wrong. If professor Brailsford told us that a nibble is a ***Decimal digit*** represented by four bit pattern, this would been so much simpler to understand. But maybe it is a language gap, or maybe i missed it. "oops was in a previous video" Basicly when people start to talk about registries and bit shifts i just get confused and suddenly i am lost LoL Well this is the punishment for starting programming in high level languages ;)

[@JmanNo42]

The original "idea" use was probably for the first digital "binary" cashregistries, they may even kept the mechanical digitroller parts "no LCD back then" and had the digit roller motors turn/roll, according to electrical BCD encoding? It seem i have some recollection of it afterall.

[@clonatul1]

Nice, but how do you convert from decimal to binary?

[@naaj100]

just reverse the process

[@clonatul1]

and how do you know when to subtract 3 from the value of the nibble?

[@kindlin]

Converting back is just dividing by reducing powers of 2. It's really too easy.

[@clonatul1]

ok, let's take 42 which is 101010 in binary, when you converted to bcd it becomes 0100 0010, the computer doesen't see decimal so how does it convert 0100 0010 to 101010?

[@joeshoesmith]

Great question, feels fiendishly difficult on a low level. It would be simple to write a script to do it, but in a woefully inefficient way.

[@MonzennCarloMallari]

When I now want to pass the time, I'll be converting 5- or 6-digit numbers to BCD by hand :3

[@ManWithBeard1990]

Realistically though you could often avoid the problem altogether by storing how many cents the client has instead of dollars. but yeah for I/O it's the only way, pretty much.

[@agmessier]

I don't understand the initial problem well, I guess. If you take the original nibble, never do any shifts, couldn't you just add 6 if greater than 9? You'd only need to use 2 nibbles.

[@Aavvv]

Double Dabble the Nibble eh

[@Avemis1]

I wonder if there was ever an "double dabble" hardware accelerator implemented. It seems to be easily parallelizable :)

[@Laurabeck329]

Almost certainly

[@whatthefunction9140]

I double-dabble my nibble everyday.

[@JmanNo42]

I guess there must be an encoding for the decimalplace in this or?

[@JmanNo42]

BDC decimalplace anyone?

[@AgentM124]

Why can't you just shift one more and add 6 instead of add 3 and shift?

[@hedgechasing]

Agent M because it wouldn’t be contained within the single nibble. Each nibble receives its own addition circuit and the carries are not connected. Adding three before the shift allows that to happen. Furthermore, the entire process of adding three can be completely circumvented just implementing a lookup table in hardware so that 0-4 become themselves but then 5 goes to 8, 6 to 9 etc and because it’s all within a nibble you don’t need any fancy circuits just a lookup table/rom.

[@AgentM124]

ChazDoesMinecraft ah I see. Thanks for the explanation.

[@FrodorMov]

I must be missing something. How is this better than a circuit that checks for larger than 10 and then add 6; without all the iterative shifting

[@hedgechasing]

Fz it only makes sense if you look at what happens with more than two digit numbers. If you implement it this way, each nibble gets its own dedicated adder and he circuit is infinitely expandable.

[@CronosXIIII]

Because imagine trying if the number you were trying to convert was 100. 0000 0110 0100 (100 binary) 0001 0000 0000 (100 bcd) How does the rule that if a byte is > 9, just add 6, apply here?

[@TheTwick]

Double, dabble, toil and trouble; Fire burn and caldron bubble. WS?

[@philrod1]

Well, I thought this was completely obvious ... after Professor Brailsford explained it.

[@jan4946]

It also works with 1101 :) Is that your Rubik's Cube?

[@damnloveless]

Are these actual terms? He uses them so casually....

[@LukiaTheTrue]

Would you please FFS activate auto subtitles ?.... thank you !

[@Computerphile]

They are active, sadly they are not compatible with 'community subtitles' which are always active. The good news is Prof Brailsford does his own subtitles so there will be some excellent subtitles soon >Sean

[@FennecTECH]

Bank balance is almost always represented as An intiger. 1.00 = 100

[@RowenStipe]

Sir, I'll have you know that I have 3.24 in my bank account right now!

[@TheTexasCanuck]

6:22 it goes to 11

[@alienym0us99]

Double Dabble not Double Dribble??? Did Double Dribble use Double Dabble???

[@anastasiadunbar5246]

Double Dab

[@Cold_Ham_on_Rye]

I still don't grasp what is wrong with 1010. Like... there it is 1010 ... someone please explain. I'm not comp sci and I'm a bit drunk

[@SenorQuichotte]

Don't be lazy learn hex

[@thebigmacd]

Why not just start with an 8-bit register with a 4-bit binary number in the rightmost nibble, and add 6 if the value is 10 or greater? No shifts required, the 8-bit register now contains the tens and units. Done.

[@CronosXIIII]

Because that doesn't work the second you try to convert a bigger number. Try converting 0000 0110 0100 to 0001 0000 0000 using that method. It doesn't work.

[@urinater]

Nibble nobble

[@evanm2024]

I'm sure that there are more advanced applications that make it worthwhile... but this is just a glorified way of adding six... 10+6=16=0x10. 11+6=17=0x11, etc. More generally, if X is your binary number, you take the three most significant bits, i.e. you divide by two, then add 3, then shift once (i.e. multiply by two), or equivalently, (3 + X/2)*2 =6+X. Yes, I know you need to modify this argument slightly when X is odd, but it still works.

[@juvinegazar3139]

Please explain why, 0101+0011=1000 @8:20..

[@lj_fin827]

the most british video an the internet

[@Gooberpatrol66]

We should just switch from decimal to binary, tbh

[@afreen5058]

I've never felt more distant from the English language in my life.

[@DavidHume-Educator]

This man convinces me that a really good memory is the difference between just being smart and being a genius. No matter how smart you are, if you can't keep a large number of things clear in your mind at the same time, you are limited in what you can do. Elon Musk, near perfect memory, is a case in point.

[@klogechris]

well Albert Einstein was known for his extremely bad memory. He wrote everything down otherwise he would forget it. His teacher even proclaimed that he had a memory like a sieve.

[@daxicous]

I've never heard elon musk having near perfect memory but I dont think he should be considered a genius anyway

[@stone_pilot]

I find it frustrating that this wasn't helpful to me. Edit*: I ended up watching the 20 minute video from organic chemistry tutor and even though he doesn't call it double dabble, that's the method he uses, so if anyone else found this video unhelpful, consider checking out that one.

[@jakobalbrecht1154]

.10 your current bank balance

[@andrewkelley7062]

Abracadabra

[@KoenNaarding]

Ten cents, my current account balance ; _ ; Rude

[@ashishpatel350]

🤣🐸👌🏽

[@sofia.eris.bauhaus]

just abolish decimal, duh..

[@chrisakaschulbus4903]

they should once in a while focus on the more exciting... "nibbles". then nobody would think they are crazy nerds, that one day will help skynet to understand what decimal numbers are