Should Devs know how maths works?
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I learned it in one of my Freshman/Sophomore level CS classes. My lecturer for the class didn't know that 0.1 (decimal) was a repeating decimal in binary. :doh: After the lecture I had to demonstrate it by working the division longhand through 2 or 3 repeats and then by converting the repeating decimal back into a fraction.
3x12=36 2x12=24 1x12=12 0x12=18
:| on what university you graduated?
In soviet Russia code debugs You!
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Danny Martin wrote:
We take it for granted that those beige boxes (or white, shiny ones in my case :O ) know that 2 + 2 = 4
Trouble is that they don't. They might know that 010 + 010 = 100, but not the 2 + 2 = 4.
I wanna be a eunuchs developer! Pass me a bread knife!
Mark Wallace wrote:
010 + 010 = 100
No. 010 + 010 = 20 010b + 010b = 100 ;P
In soviet Russia code debugs You!
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Hi Guys, I am doing a bit of research and was just wondering... How many programmers know how a computer does math? We take it for granted that those beige boxes (or white, shiny ones in my case :o) know that 2 + 2 = 4, but how many devs know how they work it out? How many care? Should we know? If you know, how did you find out, and when / under what circumstances etc. I learned Boolean Logic in the nineties while working with 68k assembler, and it was a real eye opener. What are the teams thoughts? Danny
Kind of in response to the php string vs. int earlier... We had a QA team member the other day that was extracting 2 values from a screen. It should be the same value. One value was retrieved as a string that was formatted to decimal places (1.00). The other was a floating point value that their testing tool displayed with only a single decimal place (1.0). Their comparison was saying that the two values were different. I do not use the testing tool myself but it could have been failing due to string vs. float or even string vs. string where the decimal places were different. I am not sure what they did to solve it, but this seemed like a really basic problem that they should have hit years ago. Of course since it is a float, the actual value may have been .999999999999. Who knows? P.S. I hate floats.
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Danny Martin wrote:
nineties while working with 68k assembler
Whippersnapper! Early 80s, z80 & 6502. Ah, the days of knowing 1's and 2's complement, and hexadecimal... Iain.
I am one of "those foreigners coming over here and stealing our jobs". Yay me!
the ancient one, he who speaks of floppy disks I first used the PDP-7
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Eddy Vluggen wrote:
Ideally a dev would learn to do additions in a different representation than decimal.
I think it's not really dev work. I learned this in high school (with electronics specialization) on microprocessors classes. And again on university on classes about assembler x86 and 51 miprocessors. So this is really another job. Unless you are developing mP, mC apps in assebly :)
In soviet Russia code debugs You!
n.podbielski wrote:
I think it's not really dev work
Math is not your work, it's knowledge that makes you better at your work. It's not required for drawing forms or manipulating Xml, but it helps a lot when you need to implement/understand an algorithm. Try writing your own
BigIntin .NET 2, or Google for 'encryption' in VB6 - the latter will most likely give examples that perform a calculation on a string. It helps in understanding that a Guid is merely a large number, why there's a difference in text-encodings, and why theoris used in C# to "add" enums together (BindingFlags.Public | BindingFlags.Instance)Bastard Programmer from Hell :suss:
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Nemanja Trifunovic wrote:
What Every Computer Scientist Should Know About Floating-Point Arithmetic
:omg: I am SO glad I'm not a Computer Scientist... My knowledge of this is totally binary - I only know a 'bit'. ;) Danny
Danny Martin wrote:
I am SO glad I'm not a Computer Scientist...
Me too!! And actually every person I've ever met that calls him/herself a Computer Scientist (with a BS in CS) has been a complete and pretentious twat! :-D
The environment that nurtures creative programmers kills management and marketing types - and vice versa. - Orson Scott Card
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:| on what university you graduated?
In soviet Russia code debugs You!
Does it really matter. Y2K cash flinging had gutted the dept and most of the entry level courses were being taught by moonlighters. This one was confused because his calculator
idiot boxhad rounded the last displayed digit from 0 to 1, making him think it wasn't repeating. :doh:3x12=36 2x12=24 1x12=12 0x12=18
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Hi Guys, I am doing a bit of research and was just wondering... How many programmers know how a computer does math? We take it for granted that those beige boxes (or white, shiny ones in my case :o) know that 2 + 2 = 4, but how many devs know how they work it out? How many care? Should we know? If you know, how did you find out, and when / under what circumstances etc. I learned Boolean Logic in the nineties while working with 68k assembler, and it was a real eye opener. What are the teams thoughts? Danny
Anyone who write software need to know a little to be able to deal correctly with float. Too many supposed devs tell me "How come my number is not 0?!?!?" :rolleyes: I might be biased though, since I work mostly on embedded system...
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What I'm saying here, and is being echoed by others, is that you don't need to know that a computer uses AND / XOR to do addition in order to write a function which adds two numbers. I believe there are many devs out there that don't know, don't need to know and quite frankly could care less. You don't need to know how to write a for next loop in assembler in order to write one in another, higher level language, but if you 'do' know how it works at the machine level I think it gives you a greater insight into how those higher level languages do their thing. it certainly helped me to understand what was going on under the hood. Danny
I agree with the don't know and don't need to know parts, but I think a developer who could "care less" about how his code is actually being executed on the machine is not going to be a very good developer. In my experience good developers ALWAYS care about how things work because that's the only way to make things work better. And isn't that what development is really about, building things to make the world work better? Don't get me wrong, a developer who prioritizes getting his work done over figuring out how it works is a responsible developer. There are many things that I don't understand, wish I had time to investigate more fully, but probably never will. This isn't because I "care less" it's because I prioritize my activities and knowing how some particular thing works may be a lower priorty item in my queue. Personally, I am a 10+ year developer who's had quite a bit of success. I stopped taking math classes in High School with Pre-Calculus. I major'd in communications with only a minor in Computer Science that required no mathematics training. My years learning the in's and out's of the TV news business has served me better than if I spent those years learning how maths work as I now write software for the TV news business. My understanding of the business is much more important in creating useful products than understanding how a computer adds two numbers under the covers. BUT, when I have to dig deeper I do so willingly...when it came time to understand a hex dump I reprioritized my queue and learned how to do it etc. So my answer to the original question is devs should know how maths work if they've ever needed to know how maths work. Sean
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Hi Guys, I am doing a bit of research and was just wondering... How many programmers know how a computer does math? We take it for granted that those beige boxes (or white, shiny ones in my case :o) know that 2 + 2 = 4, but how many devs know how they work it out? How many care? Should we know? If you know, how did you find out, and when / under what circumstances etc. I learned Boolean Logic in the nineties while working with 68k assembler, and it was a real eye opener. What are the teams thoughts? Danny
Programmers SHOULD know how a computer does math. That's why this is covered in college courses. A few examples: 1. Overflow and underflow. If a clueless, self-taught "programmer" assumes an int is an "integer", they're oblivious to the possibility of overflow, and their code is a time bomb, waiting for a case that goes over the 32-bit limit. 2. Floating-point arithmetic. I've met programmers that think (floatNum / 7) * 7 == floatNum. They're oblivious to the fact that floating-point numbers are an approximation of real numbers that aren't a power of 2. 3. Efficiency. Programmers that have a clue how a computer does math know things, such as floating-point multiplication is faster than division, and integer math is faster than floating-point math. 4. Round-off error. The limited precision of computer math causes the order of operations to be significant, even when mathematically the order doesn't matter.
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By my experience that also accounts for a few new posts in the coding horrors section, usually committed by somebody who is totally unaware of what's so horrible about it. And, my personal favorite, experienced developers quickly looking the other way and leaving the dirty work to that rambling idiot who keeps ranting about how important that stuff is.
"I just exchanged opinions with my boss. I went in with mine and came out with his." - me, 2011 ---
I am endeavoring, Madam, to construct a mnemonic memory circuit using stone knives and bearskins - Mr. Spock 1935 and me 2011I might fit into the above category. I code and I take it very seriously. I did not start my working like as a coder, in fact far from it. I have no formal education as a coder but I have taught myself enough to get where I am. I constantly strive to improve my code and expand what I know. On those very rare occassions when I have free time I read as many tech articles and/or books on coding and theory as I can. But my math skills are still pretty poor. I know this and I accept that I will have to do crunchtime research every time a hex issue or binary issue pops up. No, it's not the best approach but it can work. I am at my job six years now and am writing some pretty important software for my client. FWIW, I am also thankful that there are folks smarter than I am willing to share what they know about these topics. Please remember that not everyone who doesn't do well at math is a script-kiddy slacker parasite just waiting to have you do their work for them. I realize that is NOT what you said, but I have to admit to frequently getting that feeling from many of the posts here on different topics. Maybe you math folks are just smarter than us none-too-good at math folks? I am willing to concede that point. But I would wager that many of us DO know that a clear understanding of the basics of computer math is important and that we DO try. We don't always succeed, but we try. Kurt
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the ancient one, he who speaks of floppy disks I first used the PDP-7
Data General 1401 as best I can recall. Had to toggle in a JPUN to kickstart the KSR terminal.
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Iain Clarke, Warrior Programmer wrote:
Whippersnapper!
Mewling infant! Mid 60s on this machine[^]; I'm not in any of the photos but the dark haired guy in the first picture was my shift leader.
The best things in life are not things.
You got me beat. Late '60s PDP-8/I PDP-8/I display[^] But then made up for it by being a computer operator for three Univac 418's. Univac 418's[^] That's me, mid '70s, with three computers to oversee, I had to be fast enough to be two places at once :laugh: Later, when I wrote the Biorhythm cartridge for the Bally Home Arcade (later Astrocade), I had to write a multi-byte binary multiply and divide math package to do the date calculations. I wish I had known how to do that in high school on the PDP-8/I, I ended up using the EAE (Extended Arithmetic Element) hardware to do date calculations. Turns out, every once in a while, a divide would take too long and the processor would then miss interrupts (really, really bad for the timesharing system it was running).
Psychosis at 10 Film at 11
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Hi Guys, I am doing a bit of research and was just wondering... How many programmers know how a computer does math? We take it for granted that those beige boxes (or white, shiny ones in my case :o) know that 2 + 2 = 4, but how many devs know how they work it out? How many care? Should we know? If you know, how did you find out, and when / under what circumstances etc. I learned Boolean Logic in the nineties while working with 68k assembler, and it was a real eye opener. What are the teams thoughts? Danny
Don't all programmers start from this? http://en.wikipedia.org/wiki/File:Principia_Mathematica_theorem_54-43.png[^]
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You got me beat. Late '60s PDP-8/I PDP-8/I display[^] But then made up for it by being a computer operator for three Univac 418's. Univac 418's[^] That's me, mid '70s, with three computers to oversee, I had to be fast enough to be two places at once :laugh: Later, when I wrote the Biorhythm cartridge for the Bally Home Arcade (later Astrocade), I had to write a multi-byte binary multiply and divide math package to do the date calculations. I wish I had known how to do that in high school on the PDP-8/I, I ended up using the EAE (Extended Arithmetic Element) hardware to do date calculations. Turns out, every once in a while, a divide would take too long and the processor would then miss interrupts (really, really bad for the timesharing system it was running).
Psychosis at 10 Film at 11
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Hi Guys, I am doing a bit of research and was just wondering... How many programmers know how a computer does math? We take it for granted that those beige boxes (or white, shiny ones in my case :o) know that 2 + 2 = 4, but how many devs know how they work it out? How many care? Should we know? If you know, how did you find out, and when / under what circumstances etc. I learned Boolean Logic in the nineties while working with 68k assembler, and it was a real eye opener. What are the teams thoughts? Danny
Depends what you mean. Do you mean, "Do I know how addition and subtraction occur in 2's complement?" Do you mean, "Do I know what assembler instructions propogate the carry?" Do you mean, "Do I know how a carry-lookahead adder is implemented in logic gates?" These are pregressively deeper and deeper knowledge of how a computer does math(s). I've needed to know how 2's complement math works frequetly in my career. I've obviously had to know what assember instructions do the math and just how they work at least once or twice. I happen to know how a carry lookahead adder works, but I've never had to use that knowledge, since I prefer to keep my big clumsy fingers out of the actual hardware. The first topic were covered in detail in my CS undergrad coursework in the late '70's. The middle topic I got exposed to during a horrible machine-language project for pay in the late '70's. I'm talking M6800 machine language, 16kbytes RAM, no disk, paper tape, patch-the-binaries-because-the-source-code-didn't-fit-in-RAM, ahh-run-screaming! The third topic, I first encountered in 9th grade, when I was so bored in school that I began designing computer circuits to avoid falling asleep. I had this "Build Your Own Working Digital Computer" book. The topic was also covered in my CS coursework.
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Hi Guys, I am doing a bit of research and was just wondering... How many programmers know how a computer does math? We take it for granted that those beige boxes (or white, shiny ones in my case :o) know that 2 + 2 = 4, but how many devs know how they work it out? How many care? Should we know? If you know, how did you find out, and when / under what circumstances etc. I learned Boolean Logic in the nineties while working with 68k assembler, and it was a real eye opener. What are the teams thoughts? Danny
I do. Both kinds (integer & floating point). I learned how interger math happened back during my high school years, when my dad and I were both learning about computers. He was more into the theory and taught me how 2's complement math worked and how logic gates could be wired together to implement it. I was never taught that level of detail again. I didn't learn how the innards of an FPU worked until college, when I was asked to write a test for the FPU hardware of the college's Vaxs (apparently they failed from time to time). It even found a failure in a live system :) As for boolean logic, that was also during my high school years. Math class taught the expressions. I played with logic gates for fun outside of school. I found one of my dad's books that had circuit diagrams for the elecronics inside the gates that I studied until I understood them. My thoughts: if a developer doesn't understand the level beneath the one they program to (i.e. the one they can debug and fix), there will be times when they are completely ineffective. We don't get paid to be ineffective. Understanding two or more levels deeper won't help (unless there's the possibility of being able to debug at that level too), so isn't necessary. So, here's a joke absolutely every developer should find amusing.. How many times will this (C) loop iterate? for (float f = 0.0f; f < 1000000000.0; f = f + 1.0f) { } Note: float is a 4-byte IEEE floating point number.. pick an appropriate type in your favorite language. Please, nobody post the answer. If you don't know, go try it and figure it out for yourself.
patbob
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Might end up getting a job down here in Canberra with the customer I'm currently working on site with. If it looks more certain (and it is looking more than promising at the moment) I will need to have a chat with you about the areas (if any) to avoid living and any other Canberra advise you may have.
Michael Martin Australia "I controlled my laughter and simple said "No,I am very busy,so I can't write any code for you". The moment they heard this all the smiling face turned into a sad looking face and one of them farted. So I had to leave the place as soon as possible." - Mr.Prakash One Fine Saturday. 24/04/2004
Just stay clear of Tuggers. (Though it's been6 years since I lived there)
cheers, Chris Maunder The Code Project | Co-founder Microsoft C++ MVP
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Hi Guys, I am doing a bit of research and was just wondering... How many programmers know how a computer does math? We take it for granted that those beige boxes (or white, shiny ones in my case :o) know that 2 + 2 = 4, but how many devs know how they work it out? How many care? Should we know? If you know, how did you find out, and when / under what circumstances etc. I learned Boolean Logic in the nineties while working with 68k assembler, and it was a real eye opener. What are the teams thoughts? Danny
What I've found over the years is that "normal" developers don't need to know how the computer performs math operations. Their development software simply does the magic. Here's where the caveat comes in: "Normal" developers = Business Application Developers Over my career I've primarily done business application development. In the few cases where I was doing scientific development, all the math rules changed. In the scientific arena, you need to understand what's really going on so that you can: 1. Optimize operations 2. Guarantee accuracy to xx digits Sounds simple, but it's not. If you really think it's simple just take a look at some of the "Big Number" math software from places like MIT. You'll see that how the number is constructed and managed becomes very important. Here's an exercise to try: Write a program that will divide a 100-digit number by a 50-digit number. At a company that I used to work for (back around 1989) this was exactly the challenge made to all programmers in the company by the company President. The hook? We developed in Natural on the IBM mainframe. For those who don't know, Natural is a 4GL created to run primarily against an ADABAS DBMS. Both ADABAS and Natural are the IP of Software AG. Within the company only two programmers, myself and one other, came up with solutions to this problem. His was pretty quick but had a couple of numeric domain issues, mine was slower but I neglected to check for a zero divisor. Both of us were awarded a (rather nice) bottle of champagne for our effort (the company President really just wanted to know that he had people who would actually take up the challenge. As it turns out, more than half of the employees started, but only two of us came up with practical implementations that didn't attempt to "extend" the language or environment).
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Not everyone is like you. What you think should be important may not be important to me or the next guy. I do very well for myself in my profession (on all levels). To slight me because I don't get off on 0's and 1's is lame. Instead of talking smack about your intern and crying about it, why don't you take the time to show this person the connection between the 1's and 0's and why they are important.
-- ** You don't hire a handyman to build a house, you hire a carpenter. ** Jack of all trades and master of none.
If you are going to write software that does math then you have to know how computers represent numbers and how they do math. Both the representation of numbers and the methods used to do the calculations place limitation on what you can do and how you can do it.
